Question
Solve the following quadratic equation by formula method
$2 x^2-5 x+2=0$
$2 x^2-5 x+2=0$
✓
Answer
$
\begin{aligned}
& a=2, b=-5, c=2 \\
& x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} \\
& =\frac{5 \pm \sqrt{25-4(2)(2)}}{4} \\
& =\frac{5 \pm \sqrt{25-16}}{4} \\
& =\frac{5 \pm \sqrt{9}}{4} \\
& =\frac{5 \pm 3}{4} \\
& =\frac{5+3}{4} \text { or } \frac{5-3}{4} \\
& =\frac{8}{4} \text { or } \frac{2}{4}=2 \text { or } \frac{1}{2}
\end{aligned}
$
The solution set is $\frac{1}{2}$ and 2
\begin{aligned}
& a=2, b=-5, c=2 \\
& x=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a} \\
& =\frac{5 \pm \sqrt{25-4(2)(2)}}{4} \\
& =\frac{5 \pm \sqrt{25-16}}{4} \\
& =\frac{5 \pm \sqrt{9}}{4} \\
& =\frac{5 \pm 3}{4} \\
& =\frac{5+3}{4} \text { or } \frac{5-3}{4} \\
& =\frac{8}{4} \text { or } \frac{2}{4}=2 \text { or } \frac{1}{2}
\end{aligned}
$
The solution set is $\frac{1}{2}$ and 2
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