Question

if alpha &beeta are the zeroes of the quadratic equation polynomial
p(x)=kx^2+4x+4, such that alpha^2+beeta^2=24.find k.

Answer 1

kx^2+ 4x + 4

ax^2+ bx + c = 0
a= k
b= 4
c= 4


Sum of zeroes
alpha + beta= -b/a
= -4/k. --------- (1)

Product of zeroes
alpha*beta= c/a
= 4/k. ---------(2)



alpha^2 + beta^2= 24
(alpha + beta)^2- 2alpha*beta
(-4/k)^2- 2(4/k)= 24
16/k - 8/k = 24
16-8/k= 24
8/k = 24
k= 3


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