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First Year Math Quadratic Equations 3. Solve the following equations by completing square:(ix) 4-\frac{8}{3 x+1}=\frac{3 x^{2}+5}{3 x+1}


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3. Solve the following equations by completing square:(ix) 4-\frac{8}{3 x+1}=\frac{3 x^{2}+5}{3 x+1}

Solve the following equations.4. \sqrt{3 x+100}-x=4
Solve the following equations.4.  \sqrt{3 x+100}-x=4

Solve the following equations.4. \sqrt{3 x+100}-x=4

4. Solve by using synthetic division if(ii) 3 is the root of the equation 2 x^{3}-3 x^{2}-11 x+6=0
4. Solve by using synthetic division if(ii) 3 is the root of the equation  2 x^{3}-3 x^{2}-11 x+6=0

4. Solve by using synthetic division if(ii) 3 is the root of the equation 2 x^{3}-3 x^{2}-11 x+6=0

1. Write the following ratic equations in the standard form and point out pure ratic equations.(vi) \frac{x+1}{x+2}+\frac{x+2}{x+3}=\frac{25}{12}
1. Write the following ratic equations in the standard form and point out pure ratic equations.(vi)  \frac{x+1}{x+2}+\frac{x+2}{x+3}=\frac{25}{12}

1. Write the following ratic equations in the standard form and point out pure ratic equations.(vi) \frac{x+1}{x+2}+\frac{x+2}{x+3}=\frac{25}{12}

Q.33 Roots of ratic equation a x^{2}+b x+c=0 are imaginary and unequal if :(a) b^{2}-4 a c=0 (b) b^{2}-4 a c>0 (c) b^{2}-4 a c<0 (d) b^{2}-4 a c \geq 0
Q.33 Roots of ratic equation  a x^{2}+b x+c=0  are imaginary and unequal if :(a)  b^{2}-4 a c=0 (b)  b^{2}-4 a c>0 (c)  b^{2}-4 a c<0 (d)  b^{2}-4 a c \geq 0

Q.33 Roots of ratic equation a x^{2}+b x+c=0 are imaginary and unequal if :(a) b^{2}-4 a c=0 (b) b^{2}-4 a c>0 (c) b^{2}-4 a c<0 (d) b^{2}-4 a c \geq 0

Q.13 Roots of ratic equation 2 x^{2}+3 x+1=0 are :(a) \frac{1}{2}-1 (b) -\frac{1}{2} 1 (c) -\frac{1}{2}-1 (d) 1-1 Faisalabad Board 2013
Q.13 Roots of ratic equation  2 x^{2}+3 x+1=0  are :(a)  \frac{1}{2}-1 (b)  -\frac{1}{2} 1 (c)  -\frac{1}{2}-1 (d)  1-1 Faisalabad Board 2013

Q.13 Roots of ratic equation 2 x^{2}+3 x+1=0 are :(a) \frac{1}{2}-1 (b) -\frac{1}{2} 1 (c) -\frac{1}{2}-1 (d) 1-1 Faisalabad Board 2013

Q.42 If the sum of the roots of the equation a x^{2}-2 x+2 a=0 is equal to their product then the value of a is :(a) 1(b) 2(c) 3(d) 4
Q.42 If the sum of the roots of the equation  a x^{2}-2 x+2 a=0  is equal to their product then the value of  a  is :(a) 1(b) 2(c) 3(d) 4

Q.42 If the sum of the roots of the equation a x^{2}-2 x+2 a=0 is equal to their product then the value of a is :(a) 1(b) 2(c) 3(d) 4

Solve the following equations.9. \frac{x-a}{x+a}-\frac{x+a}{x-a}=\frac{7}{12}
Solve the following equations.9.  \frac{x-a}{x+a}-\frac{x+a}{x-a}=\frac{7}{12}

Solve the following equations.9. \frac{x-a}{x+a}-\frac{x+a}{x-a}=\frac{7}{12}

(xii) Roots of the equation 4 x^{2}-4 x+1=0 are(a) real equal(b) real unequal (c) imaginary(d) irrational
(xii) Roots of the equation  4 x^{2}-4 x+1=0  are(a) real equal(b) real unequal (c) imaginary(d) irrational

(xii) Roots of the equation 4 x^{2}-4 x+1=0 are(a) real equal(b) real unequal (c) imaginary(d) irrational

6. Find m if sum and product of the roots of the following equations is equal to a given number \lambda .(ii) 4 x^{2}-(3+5 m) x-(9 m-17)=0
6. Find  m  if sum and product of the roots of the following equations is equal to a given number  \lambda .(ii)  4 x^{2}-(3+5 m) x-(9 m-17)=0

6. Find m if sum and product of the roots of the following equations is equal to a given number \lambda .(ii) 4 x^{2}-(3+5 m) x-(9 m-17)=0

Solve the following equations.2. \sqrt{x+3}=3 x-1
Solve the following equations.2.  \sqrt{x+3}=3 x-1

Solve the following equations.2. \sqrt{x+3}=3 x-1

Solve the following equations.8. \frac{4 x+1}{4 x-1}+\frac{4 x-1}{4 x+1}=2 \frac{1}{6}
Solve the following equations.8.  \frac{4 x+1}{4 x-1}+\frac{4 x-1}{4 x+1}=2 \frac{1}{6}

Solve the following equations.8. \frac{4 x+1}{4 x-1}+\frac{4 x-1}{4 x+1}=2 \frac{1}{6}

1. Multiple Choice QuestionsFour possible answers are given for the following questions. Tick (\checkmark) the correct answer.(i) If \alpha \beta are the roots of 3 x^{2}+5 x-2=0 then \alpha+\beta is(a) \frac{5}{3} (b) \frac{3}{5} (c) \frac{-5}{3} (d) \frac{-2}{3}
1. Multiple Choice QuestionsFour possible answers are given for the following questions. Tick  (\checkmark)  the correct answer.(i) If  \alpha \beta  are the roots of  3 x^{2}+5 x-2=0  then  \alpha+\beta  is(a)  \frac{5}{3} (b)  \frac{3}{5} (c)  \frac{-5}{3} (d)  \frac{-2}{3}

1. Multiple Choice QuestionsFour possible answers are given for the following questions. Tick (\checkmark) the correct answer.(i) If \alpha \beta are the roots of 3 x^{2}+5 x-2=0 then \alpha+\beta is(a) \frac{5}{3} (b) \frac{3}{5} (c) \frac{-5}{3} (d) \frac{-2}{3}

1. Write the ratic equations having following roots.(b) 49
1. Write the ratic equations having following roots.(b)   49

1. Write the ratic equations having following roots.(b) 49

2 . Evaluate(i) \left(1-\omega-\omega^{2}\right)^{7}
 2 . Evaluate(i)  \left(1-\omega-\omega^{2}\right)^{7}

2 . Evaluate(i) \left(1-\omega-\omega^{2}\right)^{7}

4. Find p if(ii) the roots of the equation x^{2}+3 x+p-2=0 differ by 2 .
4. Find  p  if(ii) the roots of the equation  x^{2}+3 x+p-2=0  differ by 2 .

4. Find p if(ii) the roots of the equation x^{2}+3 x+p-2=0 differ by 2 .

(vii) An equation of the type 3^{x}+3^{2}-x+6=0 is a/an(a) Exponential equation(b) Radical equation(c) Reciprocal equation(d) None of these
(vii) An equation of the type  3^{x}+3^{2}-x+6=0  is a/an(a) Exponential equation(b) Radical equation(c) Reciprocal equation(d) None of these

(vii) An equation of the type 3^{x}+3^{2}-x+6=0 is a/an(a) Exponential equation(b) Radical equation(c) Reciprocal equation(d) None of these

2. Write short answers of the following questions.(viii) Define reciprocal equation.
2. Write short answers of the following questions.(viii) Define reciprocal equation.

2. Write short answers of the following questions.(viii) Define reciprocal equation.

Q.23 If x^{3}+3 x^{2}-6 x+2 is divided by x+2 then the remainder is(a) -18 (b) 9(c) -9 (d) 18
Q.23 If  x^{3}+3 x^{2}-6 x+2  is divided by  x+2  then the remainder is(a)  -18 (b) 9(c)  -9 (d) 18

Q.23 If x^{3}+3 x^{2}-6 x+2 is divided by x+2 then the remainder is(a) -18 (b) 9(c) -9 (d) 18

Q.25 If one root of an equation is -1+i then other root is(a) 1-i (b) 1+1 (c) -1-i (d) none of these
Q.25 If one root of an equation is  -1+i  then other root is(a)  1-i (b)  1+1 (c)  -1-i (d) none of these
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Q.25 If one root of an equation is -1+i then other root is(a) 1-i (b) 1+1 (c) -1-i (d) none of these

Q.20 If a polynomial x^{2}-2 x+2 is divided by x-1 then remainder is(a) 1(b) -1 (c) 0(d) 2
Q.20 If a polynomial  x^{2}-2 x+2  is divided by  x-1  then remainder is(a) 1(b)  -1 (c) 0(d) 2
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Q.20 If a polynomial x^{2}-2 x+2 is divided by x-1 then remainder is(a) 1(b) -1 (c) 0(d) 2

(viii) If b^{2}-4 a c>0 but not a perfect square then roots of a x^{2}+b x+c=0 are(a) imaginary(b) rational(c) irrational(d) none of these
(viii) If  b^{2}-4 a c>0  but not a perfect square then roots of  a x^{2}+b x+c=0  are(a) imaginary(b) rational(c) irrational(d) none of these
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(viii) If b^{2}-4 a c>0 but not a perfect square then roots of a x^{2}+b x+c=0 are(a) imaginary(b) rational(c) irrational(d) none of these

1. Find the discriminant of the following given ratic equations:(iii) 9 x^{2}-30 x+25=0
1. Find the discriminant of the following given ratic equations:(iii)  9 x^{2}-30 x+25=0
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1. Find the discriminant of the following given ratic equations:(iii) 9 x^{2}-30 x+25=0

(x) \alpha^{2}+\beta^{2} is equal to(a) \alpha^{2}-\beta^{2} (b) \frac{1}{\alpha^{2}}+\frac{1}{\beta^{2}} (c) (\alpha+\beta)^{2}-2 \alpha \beta (d) \alpha+\beta
(x)  \alpha^{2}+\beta^{2}  is equal to(a)  \alpha^{2}-\beta^{2} (b)  \frac{1}{\alpha^{2}}+\frac{1}{\beta^{2}} (c)  (\alpha+\beta)^{2}-2 \alpha \beta (d)  \alpha+\beta
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(x) \alpha^{2}+\beta^{2} is equal to(a) \alpha^{2}-\beta^{2} (b) \frac{1}{\alpha^{2}}+\frac{1}{\beta^{2}} (c) (\alpha+\beta)^{2}-2 \alpha \beta (d) \alpha+\beta

1. Find the discriminant of the following given ratic equations:(ii) 6 x^{2}-8 x+3=0
1. Find the discriminant of the following given ratic equations:(ii)  6 x^{2}-8 x+3=0
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1. Find the discriminant of the following given ratic equations:(ii) 6 x^{2}-8 x+3=0

Example I: Iff c_{k} [pare the rooss of the ratic equation
Example I: Iff  c_{k}  [pare the rooss of the ratic equation
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Example I: Iff c_{k} [pare the rooss of the ratic equation

Q.52 If \omega is complex cube root of unity then conjugate of \omega is :(a) \omega^{2} (b) -\omega^{2} (c) \omega (d) i
Q.52 If  \omega  is complex cube root of unity then conjugate of  \omega  is :(a)  \omega^{2} (b)  -\omega^{2} (c)  \omega (d)  i
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Q.52 If \omega is complex cube root of unity then conjugate of \omega is :(a) \omega^{2} (b) -\omega^{2} (c) \omega (d) i

3. Solve the following equations by completing square:(ix) 4-\frac{8}{3 x+1}=\frac{3 x^{2}+5}{3 x+1}
3. Solve the following equations by completing square:(ix)  4-\frac{8}{3 x+1}=\frac{3 x^{2}+5}{3 x+1}
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3. Solve the following equations by completing square:(ix) 4-\frac{8}{3 x+1}=\frac{3 x^{2}+5}{3 x+1}

1. Find the discriminant of the following given ratic equations:(iv) 4 x^{2}-7 x-2=0
1. Find the discriminant of the following given ratic equations:(iv)  4 x^{2}-7 x-2=0
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1. Find the discriminant of the following given ratic equations:(iv) 4 x^{2}-7 x-2=0

1. Without solving find the sum and the product of the roots of the following ratic equations.(ii) 3 x^{2}+7 x-11=0
1. Without solving find the sum and the product of the roots of the following ratic equations.(ii)  3 x^{2}+7 x-11=0
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1. Without solving find the sum and the product of the roots of the following ratic equations.(ii) 3 x^{2}+7 x-11=0

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