Question

find the value of k if the zeros of polynomial p x = k xsquare - 2 X + 5 are reciprocal of each other


please give a proper answer ​

Answer 1

Answer:

P(x) = kx² - 2x + 5

Comparing the polynomial with standard polynomial ax² + bx + c, we get

a = k, b = -2, c = 5

Let the zeroes be a and 1/a as they are reciprocal to each other.

Product of zeroes = constant term/coefficient of x² = c/a

a x 1/a = 5/k

1 = 5/k

By Cross multiplying, we get

k = 5

A polynomial in the form of ax² + bx + c where a, b and c are real numbers and a ≠ 0 is a quadratic polynomial.