Question

What is the nature of the roots of a quadratic equation 4x^2-12x?

Answer 1

Given that f(x)=4x^2-12x

So a =4, b= -12, c =0

So the discriminant, D=b^2-4ac = (-12)^2-4(4)(0)= 144>0

Since D is greater than 0 so there would be two distinct real roots.

Answer 2

SOLUTION :  

Given : 4x² - 12x - 9 = 0 .

On comparing the given equation with ax² + bx + c = 0  

Here, a = 4 , b = - 12  , c = - 9

D(discriminant) = b² – 4ac

D = (- 12)² - 4 × 4 × - 9

D = 144  + 144

D = 288

Since, D > 0  

Therefore, root of the given equation 4x² - 12x - 9 = 0 are real and distinct.

Hence, nature of roots of the quadratic equation 4x²− 12x − 9 = 0 are real and distinct.

★★ NATURE OF THE ROOTS

If D = 0 roots are real and equal  

If D > 0 roots are real and distinct

If D < 0  No real roots  

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