Posted by **meren** on Saturday, June 30, 2012 at 6:33am.

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

- maths -
**MathMate**, Saturday, June 30, 2012 at 8:52am
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

- maths -
**Reiny**, Saturday, June 30, 2012 at 9:08am
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

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