Question

If one zero of the quadratic polynomial (k²+k)x + 68x + 6k is reciprocal of the
other, find k.

Answer 1

The required answer is in attachment.

Answer 2

Answer:

k = 5

Explanation:

Given quadratic polynomial

(k²+k)x²+68x+6k

and

one zero of the given polynomial is reciprocal of the other.

Let m and 1/m are two zeroes of the polyomial.

Compare given polynomial with

ax²+bx+c, we get

a = k²+k, b = 68, c = 6k

i ) Product of the zeroes = c/a

=> m × 1/m = (6k)/(k²+k)

=> 1 = (6k)/[k(k+1)]

=> 1 = 6/(k+1)

Do cross multiplication, we get

=> k+1 = 6

=> k = 6-1

=> k = 5

Therefore,

k = 5

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