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Class 10 Math Theory of Quadratic Equations


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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
(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)α2+β2isequalto(a)α2β2(b)1α2+1β2(c)(α+β)22αβ(d)α+β(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

(ix) \frac{1}{\alpha}+\frac{1}{\beta} is equal to(a) \frac{1}{\alpha} (b) \frac{1}{\alpha}-\frac{1}{\beta} (c) \frac{\alpha-\beta}{\alpha \beta} (d). \frac{\alpha+\beta}{\alpha \beta}
(ix)  \frac{1}{\alpha}+\frac{1}{\beta}  is equal to(a)  \frac{1}{\alpha} (b)  \frac{1}{\alpha}-\frac{1}{\beta} (c)  \frac{\alpha-\beta}{\alpha \beta} (d).  \frac{\alpha+\beta}{\alpha \beta}

(ix)1α+1βisequalto(a)1α(b)1α1β(c)αβαβ(d).α+βαβ(ix) \frac{1}{\alpha}+\frac{1}{\beta} is equal to(a) \frac{1}{\alpha} (b) \frac{1}{\alpha}-\frac{1}{\beta} (c) \frac{\alpha-\beta}{\alpha \beta} (d). \frac{\alpha+\beta}{\alpha \beta}

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.Findpif(ii)therootsoftheequationx2+3x+p2=0differby2.4. Find p if(ii) the roots of the equation x^{2}+3 x+p-2=0 differ by 2 .

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

2.Evaluate(i)(1ωω2)7 2 . Evaluate(i) \left(1-\omega-\omega^{2}\right)^{7}

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

1.Withoutsolvingfindthesumandtheproductoftherootsofthefollowingraticequations.(ii)3x2+7x11=01. Without solving find the sum and the product of the roots of the following ratic equations.(ii) 3 x^{2}+7 x-11=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

6.Findmifsumandproductoftherootsofthefollowingequationsisequaltoagivennumberλ.(ii)4x2(3+5m)x(9m17)=06. 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

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