Quadratic Equation Example Using Quadratic Formula

Find the roots of the equation y = m²+7m+10 using the general formula, and show your working. The first thing to do is to set y = 0 to find the roots. Then identify the coefficients, a, b, and c, which is extremely simple.

This is the first coefficient.

This is the second coefficient.

This is the third coefficient.

Plug all the numbers into the general formula to find the roots. Always start the calculation with the discriminant first to determine if the roots are going to be real or imaginary. Also do not forget that -b in the general formula really means -1 multiplied by b, so if b happened to be a negative number then -1 × -b = +b. It becomes positive. Students often trip up here, so as a result I have shown -1 multiplied by b to show what is happening here.

As you can see, it is a simple calculation.

These are the solutions for x.