Question

Find the discriminant of the following equation2x2+x-4=0

Answer 1

Solution:-

:- Given equation

$\rm \implies \: 2 {x}^{2} + x - 4 = 0$

To find the discriminant use use this formula

$\rm \to \:D = {b}^{2} - 4ac$

So now compare with

$\rm \implies \: a {x}^{2} + bx + c = 0$

We get

$\rm \implies \: a = 2,b = 1 \: and \: c = - 4$

put the value on formula

$\rm \implies\:D = {b}^{2} - 4ac$

$\rm \implies \: D = (1)^{2} - 4 \times 2 \times - 4$

$\rm \implies \: D = 1 + 32$

$\rm \implies \: D = 33$

So Discriminant (D) = 33

More step find the value of x by quadratic formula

:- Formula

$\rm \implies \: x = \dfrac{ - b \pm \sqrt{D } }{2a}$

$\rm \implies \: a = 2,b = 1 \: ,\: c = - 4 \: \: and \: D = 33$

$\implies \rm \: x = \dfrac{ - 1 \pm \sqrt{33} }{2 \times 2}$

$\rm \implies \: x = \dfrac{ - 1 + \sqrt{33} }{4} \: and \: x = \dfrac{ - 1 - \sqrt{33} }{4}$

So value of x is

$\rm \implies \: x = \dfrac{ - 1 + \sqrt{33} }{4} \: and \: x = \dfrac{ - 1 - \sqrt{33} }{4}$

Answer 2

Answer:

GIVEN

quadratic equation

2x²+x-4=0

To Find

Discriminant

Solution

For a quadratic equation ax²+ bx+c = 0

⇒ discrimant (D) = b²-4ac

put the value of given quadratic equation in the formula of discriminant.

D = 1²- 4 x 2 x (-4)

D= 1 +32

D= 33

if D > 0, then the quadratic equation have real and unequal roots.