Solve the following quadratic equations. 3 x^2-7 x+5=0 - Vidyadip

Question

Solve the following quadratic equations.
$3 x^2-7 x+5=0$

✓

Answer

Given equation is $3 x^2-7 x+5=0$
Comparing with $a x^2+b x+c=0$, we get
$
a=3, b=-7, c=5
$
Discriminant $=b^2-4 a c$
$
\begin{aligned}
& =(-7)^2-4 \times 3 \times 5 \\
& =49-60 \\
& =-11<0
\end{aligned}
$
So, the given equation has complex roots.
These roots are given by
$
\begin{aligned}
x & =\frac{-\mathrm{b} \pm \sqrt{\mathrm{b}^2-4 \mathrm{ac}}}{2 \mathrm{a}} \\
& =\frac{-(-7) \pm \sqrt{-11}}{2(3)} \\
x & =\frac{7 \pm \sqrt{11} \mathrm{i}}{6}
\end{aligned}
$

$\therefore$ the roots of the given equation are $\frac{7+\sqrt{11} i}{6}$ and $\frac{7-\sqrt{11} i}{6}$

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