Find the roots of each of the following equations, if they exist, by applying the quadratic formula:

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

Open in App

Solution

The given equation is $2 x^{2} + x - 4 = 0$ .

Comparing it with $a x^{2} + b x + c = 0$ , we get

a = 2, b = 1 and c = −4

∴ Discriminant, D = $b^{2} - 4 a c = {(1)}^{2} - 4 \times 2 \times (- 4) = 1 + 32 = 33 > 0$

So, the given equation has real roots.

Now, $\sqrt{D} = \sqrt{33}$

$∴ α = \frac{- b + \sqrt{D}}{2 a} = \frac{- 1 + \sqrt{33}}{2 \times 2} = \frac{- 1 + \sqrt{33}}{4} β = \frac{- b - \sqrt{D}}{2 a} = \frac{- 1 - \sqrt{33}}{2 \times 2} = \frac{- 1 - \sqrt{33}}{4}$

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

Suggest Corrections

Similar questions

x + \frac{1}{x} = 3, x \neq 0

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$3 x^{2} - 2 x + 2 = 0$

2 x^{2} - 2 \sqrt{2} x + 1 = 0

2 x^{2} + a x - a^{2} = 0

4 x^{2} + 4 b x - (a^{2} - b^{2}) = 0

Join BYJU'S Learning Program