Question

Travis wants to solve a quadratic equation. Since his equation cannot be factored, Travis has to graph the equation and approximate the solution(s). Which of the following could be the equation that Travis is trying to solve?

A. 4x^2+9x-9=0
B. 2x^2+7x-5=0
C. 5x^2+x-6=0
D. 3x^2-2x-21=0

Answer 1

The correct answer is B.

Explanation:

In order to find this, calculate out the discriminant for each of the following equations. If the discriminant is a perfect square, then it can be factored.

Discriminant = b^2 - 4ac

The only of the equations that does not yield a perfect square is B. The work for it is done below for you.

Discriminant = b^2 - 4ac

Discriminant = 7^2 - 4(2)(-5)

Discriminant = 49 + 40

Discriminant = 89

Since 89 is not a perfect square, we cannot factor this.

Answer 2

Option B is correct.

Explanation:

Given that Travis wants to solve a quadratic equation. Since his equation cannot be factored, Travis has to graph the equation and approximate the solution(s).

we have to find the equation that Travis is trying to solve.

The equation which Travis trying to solve can't be factored therefore we have to find the equation which can't be factored i.e whose determinant is non-perfect square

`4x^2+9x-9=0`

`D=b^2-4ac=9^2-4(4)(-9)=81+144=225`

which is a perfect square.

`2x^2+7x-5=0`

`D=7^2-4(2)(-5)=49+40=89`

which is not a perfect square.

`5x^2+x-6=0`

`D=1^2-4(5)(-6)1+120=121`

which is a perfect square.

`3x^2-2x-21=0`

`D=(-2)^2-4(3)(-21)=4+252=256`

which is a perfect square.

Hence, the only equation whose discriminant is not a perfect square i.e the only equation which can't be factored is
`2x^2+7x-5=0`

∴ Option B is correct.