Question

If one zero of the polynomial p(x)=(k+4)x2+13x+3k is reciprocal of the other, then the value of ‘k’ ???

Answer 1

p(x) = (k+4)x^2+13x+3k

here,

a = ( k+4 )

b = ( 13 )

c = ( 3k )

➡Assume one zero of the polynomial is ' u ' (instead of Alpha.)

➡Another zero of the polynomial is ' 1/u ' (instead of beta) as other zero is the reciprocal.

we know that,

(Alpha) × (beta) = c/a

u × 1/u = 3k / k+4

3k / k+4 = 1. ( as ' u ' gets cancelled with ' 1/u ' )

3k = k+4

2k = 4

k = 2

Hence the value of ' k ' is ' 2.'

Hope it helps!☺