Question

Solve quadratic equation using the quadratic formula. 3x^2 - 3x - 4 = 0

Quadratics
ANSWERED
asked 2020-11-24
Solve quadratic equation using the quadratic formula. \(\displaystyle{3}{x}^{{2}}-{3}{x}-{4}={0}\)

Expert Answers (1)

2020-11-25
The standard quadratic equation is: \(\displaystyle{a}{x}^{{2}}+{b}{x}+{c}={0}\)
Quadratic formula is: \(\displaystyle{x}=\frac{{−{b}\pm\sqrt{{{b}^{{2}}−{4}{a}{c}}}}}{{{2}{a}}}\)
Here, a=3, b=−3 and c=−4
So,
\(\displaystyle{x}=\frac{{-{3}{\left(-{3}\right)}\pm\sqrt{{{\left(-{3}\right)}^{{2}}-{4}\times{3}\times{\left(-{4}\right)}}}}}{{{2}\times{3}}}\)
\(\displaystyle{x}=\frac{{{3}\pm\sqrt{{{9}+{48}}}}}{{6}}\)
\(\displaystyle{x}=\frac{{{3}\pm\sqrt{{57}}}}{{6}}\)
Therefore, solutions are
\(\displaystyle{x}=\frac{{{3}+\sqrt{{57}}}}{{6}}{\quad\text{and}\quad}{x}=\frac{{{3}-\sqrt{{57}}}}{{6}}\)
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