Question

If a, B are zeroes of the quadratic polynomial
p(x) = kx2 + x - 6 such that a+ B2 = 25, find the
value of k.​

Answer 1

Answer:

Step-by-step explanation:

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