Question

The quadratic formula gives which roots for the equation 2x^2 + x - 6 = 0?

Answer 1

The roots are
`x = ((3)/(2), -2)`, which is given by option C.

Explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

`ax^(2) + bx + c, a\\eq0`.

This polynomial has roots
`x_(1), x_(2)` such that
`ax^(2) + bx + c = a(x - x_(1))*(x - x_(2))`, given by the following formulas:

`x_(1) = (-b + √(\Delta))/(2*a)`

`x_(2) = (-b - √(\Delta))/(2*a)`

`\Delta = b^(2) - 4ac`

In this question, we have that:

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

Which is a quadratic equation with
`a = 2, b = 1, c = -6`. So

`\Delta = 1^(2) - 4*2(-6) = 1 + 48 = 49`

`x_(1) = (-1 + √(49))/(2*2) = (6)/(4) = (3)/(2)`

`x_(2) = (-1 - √(49))/(2*2) = (-8)/(4) = -2`

So the roots are
`x = ((3)/(2), -2)`, which is given by option C.