Find the roots of the quadratic equations by applying the quadratic formula.
$2x^2 - x + 4 = 0$

Given:

Given quadratic equation is $2x^2-x +4 = 0$.

To do:

We have to find the roots of the given quadratic equation.

Solution:

$2x^2-x + 4 = 0$

The above equation is of the form $ax^2 + bx + c = 0$, where $a = 2, b = 1$ and $c = - 4$

Discriminant $\mathrm{D} =b^{2}-4 a c$

$=(1)^{2}-4 \times 2(-4)$

$=1+32$

$=33$

$\mathrm{D}>0$

Let the roots of the equation are $\alpha$ and $\beta$

$\alpha =\frac{-b+\sqrt{\mathrm{D}}}{2 a}$

$=\frac{-1+\sqrt{33}}{4}$

$\beta =\frac{-b-\sqrt{\mathrm{D}}}{2 a}$

$=\frac{-1-\sqrt{33}}{4}$

Hence, the roots of the given quadratic equation are $\frac{-1+\sqrt{33}}{4}, \frac{-1-\sqrt{33}}{4}$.

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Updated on: 10-Oct-2022

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