What is the nature of roots of the quadratic equation 4x²− 12x − 9 = 0?
Answers
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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Answer :
The nature of roots of quadratic equation 4x² - 12x - 9 = 0 are real and distinct.
Step-by-step explanation :
4x² - 12x - 9 = 0
On comparing the given equation with ax² + bx + c = 0.
We have ;
a = 4
b = 12
c = -9
We know that ;
D ( Discriminant ) = b² - 4ac
D = (12)² - 4 * 4 * (-9)
D = 144 + 144
D = 288
Since, D > 0
Therefore, the nature of roots of given equation are real and distinct.