Question

if one zero of the quadratic polynomial 4xsquare + 5x+ gama be reciprocal of another zero, find the value of gama.

Answer 1

4x²+5x+γ=4(x-k)(x-1/k)
=4x²-4(k+1/k)+1
Equate coefficients of terms:
for x²: 4=4
for x: -4(k+1/k)=5
for constant term: γ=1

So the equation is:
4x²+5x+1=0
(4x+1)(x+1)=0

Answer 2

let the roots be p and 1/p

We know that for ax^2 + bx + c = 0
the sum of the roots = -b/a
product of roots = c/a

so in our case, product of the roots = gamma/4
but the product of roots = p(1/p) = 1
so
gamma/4 = 1

gamma = 4