Question

Solve the quadratic equation 2x^2 + x - 6 = 0, using the quadratic formula.

Answer 1

To solve the quadratic equation 2x^2 + x - 6 = 0, the quadratic formula is applied, yielding two roots, which are 1.5 and -2.

Step-by-step explanation:

To solve the quadratic equation 2x^2 + x - 6 = 0, we will use the quadratic formula, which is:

x = (-b ± √(b^2 - 4ac))/(2a)

Here, a = 2, b = 1, and c = -6.

Plugging these values into the quadratic formula, we get:

x = (-(1) ± √((1)^2 - 4×(2)×(-6)))/(2×(2))

x = (-1 ± √(1 + 48))/4

x = (-1 ± √(49))/4

x = (-1 ± 7)/4

So, the two solutions are:

x = (-1 + 7)/4 = 6/4 = 1.5

x = (-1 - 7)/4 = -8/4 = -2

The roots of the equation are 1.5 and -2.