Question

Solve the following quadratic equations by using formula method.
m² – 3m –10 = 0

Answer 1

Given: m² – 3m –10 = 0
On comparing this equation with ax² + bx + c = 0, we get:
a = 1, b = –3 and c = –10
For the quadratic equation ax² + bx + c = 0, we know that the quadratic formula is

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
In the given equation, the variable is m.
On substituting a = 1, b = –3 and c = –10, we get:

$$\begin{gathered} m=\frac{-\left(-3\right)\pm \sqrt{{\left(-3\right)}^2-4\times 1\times \left(-10\right)}}{2\times 1} \\ =\frac{3\pm \sqrt{9+40}}{2} \\ =\frac{3\pm \sqrt{49}}{2} \\ =\frac{3\pm 7}{2} \\ =\frac{3+7}{2},\frac{3-7}{2} \\ =\frac{10}{2},\frac{-4}{2} \\ m=5,-2 \end{gathered}$$

Thus, the solution of the given quadratic equation is m = 5, –2.