Question

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

Quadratics
ANSWERED
asked 2021-02-09
Solution to quadratic equation Quadratic formula -2 Examples with solution and checking

Answers (1)

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.

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