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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

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.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

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

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.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. 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}

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

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.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

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

(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

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

(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

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

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

### 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

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}

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

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