Question

If A and B are the zeros of the quadratic polynomial f(x)=kx²+4x+4 such the
${ \alpha }^{2} + { \beta }^{2} = 24$
Find the value of k​

Answer 1

ANSWER

α,β roots of f(x)=kx²+4x+4

Given α²+β²=24

We know α+β= a/−b

= k/−4

αβ= a/c

= k/4

(α+β)² =α²+β²+2αβ

( k/−4 )² =24+2( k/4 )

(-4²/k²) =24+2( k/4 )

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, 2/3

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Answer 2

Answer:

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