Question

# Solution to quadratic equation Quadratic formula -2 Examples with solution and checking

Solution to quadratic equation Quadratic formula -2 Examples with solution and checking

2021-02-10

The quadratic formula for an equation $$\displaystyle{a}{x}^{{2}}+{b}{x}+{c}={0}\ {i}{s}\ {g}{i}{v}{e}{n}\ {b}{y}\ {x}=\frac{{-{b}\pm\sqrt{{{b}^{{2}}-{4}{a}{c}}}}}{{2}}{a}$$
Consider the quadratic equation $$\displaystyle{x}^{{2}}+{5}{x}+{6}={0}.$$
Compare the equation with standard form $$\displaystyle{a}{x}^{{2}}+{b}{x}+{c}={0}.$$
Here, $$a=1, b=5\ and\ c=6.$$
Evaluate the solutions of the quadratic equation as follows.
$$\displaystyle{x}=\frac{{-{5}\pm\sqrt{{{5}^{{2}}-{4}{\left({1}\right)}{\left({6}\right)}}}}}{{2}}{\left({1}\right)}$$
$$\displaystyle{x}=\frac{{-{5}\pm\sqrt{{{25}-{24}}}}}{{2}}$$
$$\displaystyle{x}=\frac{{{5}\pm{1}}}{{2}}$$
$$\displaystyle{x}=\frac{{-{5}+{1}}}{{2}}{\quad\text{or}\quad}{x}=\frac{{-{5}-{1}}}{{2}}$$
$$x=-2\ or\ x=-3$$
Verification:
Substitute $$x=-2$$ in the quadratic equation and verify the solution as follows.
$$\displaystyle{\left(−{2}\right)}^{{2}}+{5}{\left(−{2}\right)}+{6}={0}$$
$$4−10+6=0$$
$$0=0$$ (True)
Thus, the solution $$x=-2$$ is verified.
Substitute $$x=-3$$ in the quadratic equation and verify the solution as follows.
$$\displaystyle{\left(−{3}\right)}^{{2}}+{5}{\left(−{3}\right)}+{6}={0}$$
$$9−15+6=0$$
$$0=0$$ (True)
Thus, the solution $$x=-3$$ is verified.