Question

15. If a and B are the zeroes of the quadratic polynomial f(0 = x 2x - 8. then find the value of (i)a-B (ii) a2+ B2 (iii) a4+b4( ii) ab2+a2b
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Answer 1

Step-by-step explanation:

α,β roots of f(x)=kx2+4x+4

Given α2+β2=24

We know α+β=a−b=k−4

αβ=ac=k4

(α+β)2=α2+β2+2αβ

(k−4)2=24+2(k4)

k242=24+2(k4)

16=24k2+8k

2=3k2+k

0=3k2+k−2

0=3k2+3k−2k−2

0=3k(k+1)−2(k+1)

0=(k+1)(3k−2)

∴k=−1,32