Question

Find the value of m if one zero of the polynomial(m^2+4)x^2+65x+4m

Answer 1

Find the value of m if one zero of the polynomial(m^2+4)x^2+65x+4m is the reciprocal of other

I think this is the complete questions

Let p( x ) = (m² + 4 )x² + 64x + 4m

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

compare p( x ) with ax² + bx + c ,

a = m² + 4 ,

b = 65 ,

c = 4m

we know that ,

product of the zeroes = c/a

p × 1/p = 4m/( m² + 4 )

1 = 4m/( m² + 4 )

m² + 4 = 4m

m² - 4m + 4 = 0

m² - 2 × m × 2 + 2² = 0

( m - 2 )² = 0

Therefore ,

m - 2 = 0 or m - 2 = 0

m = 2