Question

If α,β are the roots of the quadratic equation 2x2 – 3x – 4 = 0, find the equation
whose roots are α^2 and ,β^2.​

Answer 1

Step-by-step explanation:

2x²-3x-4=0

Consider alpha as ‘A’ and beta as ‘B’.

A+B = -b/a = 3/2

AB = c/a = -4/2 = -2

(A+B)²=A²+B²+2AB

(3/2)²=A²+B²+2×(-2)

9/4=A²+B²-4

9/4-4=A²+B²

A²+B²=(9-16)/4 = -7/4