Question

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

To Find :-

• The value of the discriminant, and with that value we have to determine the nature of the roots.

Solution :-

Quadratic equation,

√3x² + 2√2x - 2√3 = 0

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

→ Discriminant, D = b² - 4ac

According to the question,

• a = √3
• b = 2√2
• c = 2√3

Putting the given values :-

→ D = (2√2)² - 4(√3)(2√3)

→ D = 4 × 2 - 4×2×3

→ D = 8 - 24

→ D = -16

-16< 0.

So,

• There exists two imaginary roots for the given quadratic equation.

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Answer 2

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.