Using the quadratic formula, find the roots of: 4x^{2}+7x-15=0 N

Sheelmgal1p 2021-11-21 Answered
Using the quadratic formula, find the roots of: \(\displaystyle{4}{x}^{{{2}}}+{7}{x}-{15}={0}\)
Answer can be left as fractions. \(\displaystyle{x}={\frac{{-{b}\pm\sqrt{{{b}^{{{2}}}-{4}{a}{c}}}}}{{{2}{a}}}}\)

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Expert Answer

Himin1945
Answered 2021-11-22 Author has 377 answers
Step 1
The quadratic formula is used when the roots of the quadratic equation cannot solved by the factorisation method.
Step 2
Here on comparsion of the quadratic equation \(\displaystyle{4}{x}^{{{2}}}+{7}{x}-{15}={0}\) with the standard quadratic equation \(\displaystyle{a}{x}^{{{2}}}+{b}{x}+{c}={0}\), it is observed that a is 4, b is 7 and c is -15. Therefore substitute these values in the equation \(\displaystyle{x}={\frac{{-{b}\pm\sqrt{{{b}^{{{2}}}-{4}{a}{c}}}}}{{{2}{a}}}}\) to find the value of x.
\(\displaystyle{x}={\frac{{-{b}\pm\sqrt{{{b}^{{{2}}}-{4}{a}{c}}}}}{{{2}{a}}}}\)
\(\displaystyle{x}={\frac{{-{7}\pm\sqrt{{{7}^{{{2}}}-{4}{\left({4}\right)}{\left(-{15}\right)}}}}}{{{2}{\left({4}\right)}}}}\)
\(\displaystyle={\frac{{-{7}\pm\sqrt{{{49}+{240}}}}}{{{8}}}}\)
\(\displaystyle={\frac{{-{7}\pm\sqrt{{{289}}}}}{{{8}}}}\)
\(\displaystyle{x}={\frac{{-{7}\pm{17}}}{{{8}}}}\)
\(\displaystyle{x}={\frac{{-{7}+{17}}}{{{8}}}}\)
\(\displaystyle={\frac{{{5}}}{{{4}}}}\)
\(\displaystyle{x}={\frac{{-{7}-{17}}}{{{8}}}}\)
\(\displaystyle=-{3}\)
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