Question

Find the zeros of the quadratic polynomial 2x^2-10 and verify the relationship between the zeros and the coefficient

Answer 1

p(x) = 2x^2 - 10

For finding zeroes

2x^2 - 10 = 0

2x^2 = 10

2x = +- $\sqrt{10}$

x = $\sqrt{10}$ / 2 , -$\sqrt{10}$ / 2

Relationships to verify:

1. α + β = -b/a
2. αβ = c/a

Where, a = 2, b = 0, c = -10, α = $\sqrt{10}$ / 2, β = - $\sqrt{10}$/ 2

1. LHS:

α + β =  $\sqrt{10}$/ 2 -  $\sqrt{10}$/ 2 = 0

RHS:

-b/a = -0/2 = 0

LHS = RHS

    2. LHS:

αβ = $\sqrt{10}$/ 2 x -$\sqrt{10}$/ 2 = -10 / 4 = -5/2

RHS:

c/a = -5/2