Question

5. Compare the quadratic equation root3x2+2root2x-2root3=0 with ax2+bx+c=0 and find the value of the discriminant. Determine the nature of the roots. *

Answer 1

We are given the following quadratic equation,

• √3x² + 2√2x - 2√3 = 0

We are requested to find the value of the discriminant, and with that value we have to determine the nature of the roots.

We know, The discriminant of a quadratic equation in the form ax² + bx + c = 0, is given by

⇒ Discriminant, D = b² - 4ac

From the given quadratic equation, we have

• a = √3
• b = 2√2
• c = 2√3

So,

⇒ D = (2√2)² - 4(√3)(2√3)

⇒ D = 4 × 2 - 4×2×3

⇒ D = 8 - 24

⇒ D = -16

Here, The value of the discriminant is negative i.e., < 0.

Hence, There exists two imaginary roots for the given quadratic equation.

Some Information :-

• If the value of discriminant of a quadratic equation is equal to 0, then there exists equal and real roots for that quadratic equation.

• If the value of discriminant of a quadratic equation is greater than zero, then two real and distinct roots exists for that quadratic equation.

Answer 2

Answer:

We are given the following quadratic

equation.

$\sqrt{} 3x {}^{2} + 2 \sqrt{} 2x - 2 \sqrt{} 3 = 0$

We are requested to find the value of the

discriminant, and with that value we have

to determine the nature of the roots.

We know, The discriminant of a quadratic

equation in the form ax^2 + bx + c = 0, is

given by

=> Discriminant, D = b^2 - 4ac

From the given quadratic equation, we

have

• a = √3
• b = 2√2
• c = 2√3

So,

=> D = (2√2) ^2 - 4 (√3) (2√3)

=> D = 4 × 2 - 4 × 2 × 3

=> D = - 16

Here, The value of the discriminant is

negative i.e., < 0

SOME INFORMATION :-

• If the value of discriminant of a quadratic equation is equal to 0 than there exists equal and real roots for that quadratic equation.

• If the value of discriminant of a quadratic equation is greater than zero, than two real and distinct roots exists for that quadratic equation.

Step-by-step explanation:

@GENIUS