Question

If the solutions to an equation are 1/2

and 5, which of the following could be the equation? A.2x^2 +9=5 B.5x^2=11x-2 C.6x-3=0 D.2x^2=11x-5

Answer 1

D. 2x² = 11x - 5

Explanation:

We can eliminate C since that is a monomial polynomial with degree 1(highest degree of x)

All the rest are quadratic equations which will yield two solutions

A. 2x² + 9 = 5
==> 2x² = 5 - 9 ==> 2x² = -4
==> x² = -2 and since the square of a number cannot be negative, this one is not a correct choice

B. 5x²= 11x-2
Plug in x = 5:
5(5)² = 11(5) - 2
125 = 55 - 2
Left side ≠ Right side so this is an incorrect choice

That leaves D as the only correct choice

Verify by plugging in both values:
D. 2x² = 11x - 5
==> 2(1/2)² = 11(1/2) + 5
==> 2 x 1/4 = 11/2 - 5
Left side is 1/2
Right side is 11/2 - 5 = 11/2 - 10/2 = 1/2 so consistent

Plug in x = 5
2(5)² = 11(5) - 5
2 x 25 = 55 - 5

50 = 50

So both x = 1/2 and x = 5 satisfy this equation and therefore choice D is t he correct choice