Question

If one zero of the polynomial 2kx2- -4x +8 is recirpocal of the other,​

Answer 1

Let the zero be x & 1/x.

Comparing 2kx² - 4x + 8 = 0 with ax² + bx + c , we get

• a = 2k
• b = -4
• c = 8

• PRODUCT OF ZEROS

αβ = c/a [ Constant term / Coefficient of x² ]

x * 1/x = 8/2k

2k = 8

k = 4

• SUM OF ZEROS

α + β = -b/a [– Coefficient of x/ Coefficient of x²]

x + 1/x = 4/2k

x² + 1 = 4x/8

8x² - 4x + 8 = 0

Value of k → 2

Required Polynomial Eqn → 8x² - 4x + 8