AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

If a, b and c are real, then both the roots of the equation

are always:

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

Positive

Negative

Real

Imaginary

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

We are given that a, b and c are real.
The given equation is

. We are required to find the nature of the roots of this equation.
First, we will expand and simplify the given equation as

Combining the coefficients of the same powers of x, we get

.
Now, we know that the formula to calculate the discriminant D of the any algebraic equation is given by

, where a is the coefficient of

,b is the coefficient of x and c is the constant term of the equation.
Therefore, we get a = 3, b = -2 (a + b + c) and c = (ab + bc + ac) from the equation we simplified above.
Substituting these values in the formula of D, we get

we know that

Here, we can see that

is the product of 2 which is a positive integer and a total of 3 perfect squares of integers which means they are positive as well.

Hence,

we can say that the roots of the given equation are real.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!