Question

For what value of p, the sum of zeros of the quadratic polynomial x^2 −(p+6)x +2(2p+1) is half of their product

Answer 1

Answer:

Let the roots be α,β

For a quadratic equation ax

2

+bx+c=0

Sum of roots α+β=k+6⋯(1)

Product of roots αβ=4k−2⋯(2)

According to question,

α+β=

2

αβ

From (1),(2)

⟹k+6=2k−1

⟹k=7