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.

Monjur Alahi

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Salim Ahmed Kawsar

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Solution:

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

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