Question

What are the roots of the quadratic equation 0 = 2x^2 + 12x –14?

2, 12, –14
–7, 1
–1, 7
1, 6, –7
Can you explain what it is wanting or asking?

Answer 1

It is basically asking you to find where the equation crosses the d-axis. 2x^2 + 12x -14 = (x-1)(2x-14). x-1=0. x=1. 2x-14=0. 2x=14. x=7. The solution/roots/zeros would be 1 and 7

Answer 2

-7, 1

Explanation:

Given quadratic equation,

`2x^2+12x-14=0`

By middle term splitting,

`2x^2+(14-2)x-14=0`

`2x^2+14x-2x-14=0`

`2x(x+7)-2(x+7)=0`

`(2x-2)(x+7)=0`

By the zero product property,

`2x-2=0\text{ or }x+7=0`

`\implies x=1\text{ or }x=-7`

Hence, the roots of the given equation are -7 and 1.

Second option is correct.