Question

If one zero of (m^2+3)x^2+23x+8 is the reciprocal of the other,find the value of m

Answer 1

Hi ,

Let p( x) = ( m² + 3 )x² + 23x + 8 ,

Let p and 1/p are two zeroes of p( x ),

compare p( x ) with ax² + bx + c ,

a = m² + 3 ,

b = 23 ,

c = 8

we know that ,

product of the zeroes = c/a

p × 1/p = 8/( m² + 3 )

1 = 8/( m² + 3 )

m² + 3 = 8

m² = 8 -3

m² = 5

m = ± √5

I hope this helps you.

: )