Question

what is the discriminant and nature of roots of 6x²-18x-24=0​

Answer 1

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Answer 2

Answer:

• Discriminant = 900
• Equation will have two distinct real roots

Explanation:

Given, quadratic equation is

• 6 x² - 18 x - 24 = 0

As we know for a quadratic equation in the form

a x² + b x + c = 0

Discriminant is given by

• Discriminant = b² - 4 a c

And, equation have two distinct real roots when discriminant > 0; two equal real roots when discriminant = 0; and no real roots when discriminant < 0.

So,

Comparing given quadratic equation with a x² + b x + c = 0

we will get,

• a = 6 , b = -18 , c = -24

Hence, calculating discriminant

→ Discriminant, D = b² - 4 a c

→ D = ( -18 )² - 4 ( 6 ) ( - 24 )

→ D = 324 + 576

→ D = 900

Here, Discriminant of given quadratic equation is 900, that is greater than zero therefore, quadratic equation will have two distinct real roots.