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

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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Himin1945
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.
$$\displaystyle{x}={\frac{{-{b}\pm\sqrt{{{b}^{{{2}}}-{4}{a}{c}}}}}{{{2}{a}}}}$$
$$\displaystyle{x}={\frac{{-{7}\pm\sqrt{{{7}^{{{2}}}-{4}{\left({4}\right)}{\left(-{15}\right)}}}}}{{{2}{\left({4}\right)}}}}$$
$$\displaystyle={\frac{{-{7}\pm\sqrt{{{49}+{240}}}}}{{{8}}}}$$
$$\displaystyle={\frac{{-{7}\pm\sqrt{{{289}}}}}{{{8}}}}$$
$$\displaystyle{x}={\frac{{-{7}\pm{17}}}{{{8}}}}$$
$$\displaystyle{x}={\frac{{-{7}+{17}}}{{{8}}}}$$
$$\displaystyle={\frac{{{5}}}{{{4}}}}$$
$$\displaystyle{x}={\frac{{-{7}-{17}}}{{{8}}}}$$
$$\displaystyle=-{3}$$