Question

If a and b are the zeroes of the polynomial f(x)=kx 2 +4x+4 such that a 2 +b 2 =24 ,find the value of k

Answer 1

a,b are the zeros of f(x)=kx²+4x+4 and a²+b²=24
a+b=-4/k and a×b=4/k
now, a²+b²=24
or, (a+b)²-2ab=24
or, (-4/k)²-2×4/k=24
or, 16/k²-8/k=24
or, (16-8k)/k²=24
or, 16-8k=24k²
or, 24k²+8k-16=0
or, 8(3k²+k-2)=0
or, 3k²+k-2=0
or, 3k²+3k-2k-2=0
or, 3k(k+1)-2(k+1)=0
or, (k+1)(3k-2)=0
either, k+1=0; or, k=-1
or, 3k-2=0; or, k=2/3

Answer 2

a,b are the zeros of f(x)=kx²+4x+4 and a²+b²=24

a+b=-4/k and a×b=4/k

now, a²+b²=24

or, (a+b)²-2ab=24

or, (-4/k)²-2×4/k=24

or, 16/k²-8/k=24

or, (16-8k)/k²=24

or, 16-8k=24k²

or, 24k²+8k-16=0

or, 8(3k²+k-2)=0

or, 3k²+k-2=0

or, 3k²+3k-2k-2=0

or, 3k(k+1)-2(k+1)=0

or, (k+1)(3k-2)=0

either, k+1=0; or, k=-1

or, 3k-2=0; or, k=2/3