Question

What will be the nature of the roots of quadratic equation 2 x square - 4 x + 3 equal to zero

Answer 1

Answer:

Imaginary roots

Step-by-step explanation:

Given quadratic equation is [2x^2-4x+3]

As to find the nature of the roots of the given quadratic equation we need to find the discriminant.

Discriminant `D'is( b^2-4ac)

Therefore [(-4)^2-4*2*3]

[16-24]= - 8

So as the discriminant is (-8)<0

So the roots of the equation are imaginary or not real.

Answer 2

Correct Question :

What will be the nature of the roots of quadratic equation 2x² - 4x + 3 = 0.

AnswEr :

Let Assume α and β are the roots of Quadratic Equation : ax² + bx + c = 0

◑ Roots : [- b ± √(b² - 4ac)] ÷ 2a

(b² - 4ac) is called the Discriminant of the Quadratic Equation. And Nature of Roots Depends upon it.

• So there are Some Cases regarding it :

⠀⠀⠀⠀⋆ Case I: (b² – 4ac) > 0

When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive, then the roots α and β of the quadratic equation ax² + bx + c = 0 are real and unequal.

⠀⠀⠀⠀⋆ Case II: (b² – 4ac) = 0

When a, b, and c are real numbers, a ≠ 0 and the discriminant is zero, then the roots α and β of the quadratic equation ax² + bx + c = 0 are real and equal.

⠀⠀⠀⠀⋆ Case III: (b² – 4ac) < 0

When a, b, and c are real numbers, a ≠ 0 and the discriminant is negative, then the roots α and β of the quadratic equation ax² + bx + c = 0 are unequal and not real. In this case, we say that the roots are imaginary.

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• Let's Head to the Question Now :

we have Quadratic Equation 2x² - 4x + 3 = 0 in the form of ax² + bx + c = 0, Here we have

◑ a = 2 ; b = (- 4) and, c = 3

Let's Find Out Discriminant of this :

⇒ D = (b² - 4ac)

⇒ D = [(- 4)² - (4 × 2 × 3)]

⇒ D = (16 - 24)

⇒ D = - 8

჻ Discriminant Falls in the Case III, therefore roots of this Quadratic Equation is Unequal and Imaginary.

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