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Refer to the attachment
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Step-by-step explanation:
p(x)=kx²+4x+4
Roots are alpha(a) ,Beta(b)
Now we know
Sum of Roots=-b/a
a+b=-4/k
Product of Root=c/a
ab=4/k
a²+b²=24
(a+b)²-2ab=a²+b²
Put the value
(-4/k)²-2×4/k=a²+b²
16/k²-8/k=24
(16-8k)/k²=24
24k²+8k-16
Factorize it
24k²+24k-16k-16
24k(k+1)-16(k+1)
(24k-16)(k+1)
k=16/24 or k=-1
K=2/3,-1
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