5x^2+5x-2

how to find the root?

To find the roots of the quadratic equation 5x^2 + 5x - 2, you can use the quadratic formula or factoring. Here's how to use each method:

1. Quadratic Formula:
The quadratic formula can be used to find the roots (also known as solutions or zeros) of any quadratic equation in the form ax^2 + bx + c = 0.

For the equation 5x^2 + 5x - 2, where a = 5, b = 5, and c = -2, the quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values into the formula, we get:
x = (-5 ± √(5^2 - 4*5*(-2))) / (2*5)
x = (-5 ± √(25 + 40)) / 10
x = (-5 ± √65) / 10

So, the roots of the equation are:
x = (-5 + √65) / 10
x = (-5 - √65) / 10

2. Factoring:
In some cases, quadratic equations can be factored to find the roots. However, not all quadratic equations can be factored easily.

For the equation 5x^2 + 5x - 2, you can try factoring by trial and error or the AC method, but it may not yield simple integer factors. In this case, the quadratic formula is the recommended method.

By using either the quadratic formula or factoring, you can find the roots of the quadratic equation.