Question

Find the value of k, such that the quadratic polynomial kx2 + 10x + k2

– 5k has one root reciprocal

to other.​

Answer 1

Given: The polynomial kx² + 10x + k²  - 5k

To find: The value of k.

Solution:

• Now we have given the polynomial kx² + 10x + k²  - 5k .

• Let one root be a, then other root is 1/a.

• Sum of roots: a + 1/a = -10/k

• Product of roots: a(1/a) = (k²  - 5k)/k

• Solving it, we get:

               1 = k - 5

               k = 6

Answer:

             So the value of k is 6.