Question

*10. Find quadratie equation such that its roots
are square of sum of the roots and square of
difference of the roots of equation
2x^2+2 (p+q)x+p^2+q^2=0
​

Answer 1

Answer:

Given quadratic equation is 2x²+2(p+q) x+p²+q²=0

Here, a=2x²

b=2(p+q) x

C=p²+q²

$\alpha + \beta = - b \div a$

$\alpha \times \beta = c \div a$

so Alpha+beta=-(p+q)x

alpha×beta=p²+q²/2

Required equation is

$x ^{2} - \alpha + \beta x + \alpha \beta = 0$

so,

x²+(p+q)x+p²+q²/2=0

2x²+(2p+2q)x+p²+q²=0

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