# CBSE Previous Year Paper

Video solution Class 10 Math: Set 3 Q20. Quadratic Equation

#### Question: If the roots of the equation (a2 + b2) x2 – 2(ac + bd) x + (c2 + d2) = 0 are equal, prove that $$frac{a}{b}$ = $\frac{c}{d}$. #### Video Explanation #### Explanatory Answer Roots of$a2 + b2)x2 – 2(ac + bd)x + c2 + d2 = 0 are equal.

For a quadratic equation of the form Px2 + Qx + R = 0, roots are real and equal when Q2 – 4PR = 0.

In this equation P = (a2 + b2), Q = -2(ac + bd), and R = c2 + d2

Therefore, (-2(ac + bd))2 - 4(a2 + b2)( c2 + d2) = 0
i.e., 4(a2c2 + b2d2 + 2abcd) – 4(a2c2 + a2d2 + b2c2 + b2d2) = 0
= 4a2c2 + 4b2d2 + 8abcd - 4a2c2 - 4a2d2 - 4b2c2 - 4b2d2 = 0
4a2d2 + 4b2c2 - 8abcd = 0

Divide both sides of the equation by 4.
a2d2 + b2c2 - 2abcd = 0
or $\frac{a}{b}$ = $\frac{c}{d}$