Question

Find the value of the discriminant of the quadratic equation
2x2 - 4x + 3 = 0.​

Answer 1

Answer:

The required value of the discriminant is -8

Step-by-step explanation:

Given :

Quadratic equation : 2x² - 4x + 3 = 0

To find :

the value of the discriminant

Solution :

For a quadratic equation ax² + bx + c = 0 ;

Discriminant is given by, D = b²- 4ac

Comparing given quadratic equation with ax²+ bx + c = 0, we get

a = 2

b = -4

c = 3

Discriminant,

 D = (-4)² - 4(2)(3)

 D = 16 - 8(3)

 D = 16 - 24

 D = -8

Therefore, the value of the discriminant is "-8"

• So, what does it mean if the value of discriminant is less than 0?

The quadratic equation has no real roots. i.e., it has complex roots

So, 2x² - 4x + 3 = 0 has complex roots.

• The nature of roots is based on the value of discriminant.

D > 0 ; the quadratic equation has real and distinct roots

D = 0 ; the quadratic equation has real and equal roots

D < 0 ; the quadratic equation has complex roots.

Answer 2

$\bf{Answer}$

Step by step explanation:-

Given Q.E

2x² -4x +3 =0

So, first of all what is Discriminant ??

In Quadratic equation ax²+bx+c = 0

If a,b are roots of Quadratic equation

These nature of roots are determined by Discriminant

What is nature of roots?

If roots are real /complex/conjugate/equal These are called as nature of roots

So, We can find Discriminant

Discriminant of Quadratic equation is given by b²-4ac

If they given any Quadratic equation We can find Discriminant by formula

D = b²-4ac

Discriminant is denoted by D

If D =0 roots are real and equal

D >0 roots are equal and real

D <0 Roots are complex &conjugate

D >0 &D is perfect square roots are rational and distint

D <0 &D is not perfect square roots are irrational &complex

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So, 2x²-4x +3 =0

D = b²-4ac

a = 2

b = -4

c = 3

D = (-4)² -4(2)(3)

D = 16 -24

D = -8

So,Discriminant of given Q.E 2x²-4x +3 =0 is -8

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Hence -8 is Discriminant roots of Quadratic equation is not real Hence This Quadratic equation has complex roots and roots are conjugate

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Hope my answer is helps to u :)

Tq :)