Question

If α and β are zeroes of a quadratic polynomial p(x) = rx^2+4x+4, Find the values of “r” if: – α^2 + β^2 = 24.

Answer 1

From the given polynomial p(x),

α + β = −4/r, and αβ = −4/r………. (1)

Since,(α + β)² = α² + β² + 2αβ

Given,   α² + β² = 24 and from equation (1).

Therefore,  (−4/r)²=24+(2×4)/r

16/r²=24+(2×4)/r

16 = 24 r² + 8r

3r² + r – 2 = 0

3r² + 3r – 2r -2 = 0

3r(r+1) – 2(r+1) = 0

(3r-2) (r+1) = 0

∴  r = 2/3   or   r = -1