Book Online Demo

Check Your IQ

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

Which of the following equations has no real roots?

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

x 2 − 4 x + 32 = 0

x 2 + 4 x − 32 = 0

x 2 − 4 x − 32 = 0

3 x 2 + 43 x + 4 = 0

answer is A.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

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

Take Free Test

Detailed Solution

It is given equations.
We know that an equation of the form

a x 2 + b x + c = 0, a ≠ 0

is called quadratic equation in one variable x, where a, b, c are constants.
Let us find the discriminant for all the given options.
We also know that if the discriminant

D = b 2 − 4 a c

is less than 0, there are no real roots for the given quadratic equation.
For option (1), the discriminant of the equation

x 2 − 4 x + 32 = 0.

Here,

a = 1, b = − 4, c = 32

D = b 2 − 4 a c = (− 4) 2 − 4 (1) (32) = 16 − 122 D < 0

Thus, the equation

x 2 − 4 x + 32 = 0

has no real roots.
For option (2), the discriminant of the equation

x 2 + 4 x − 32 = 0.

Here,

a = 1, b = 4, c = − 32 .

D = b 2 − 4 a c = 42 − 4 (1) (− 32) = 16 + 1221 D > 0

Thus, the equation

x 2 + 4 x − 32 = 0

has two distinct real roots.
For option (3), the discriminant of the equation

x 2 − 4 x − 32 = 0.

Here,

a = 1, b = − 4, c = − 32 .

D = b 2 − 4 a c = (− 4) 2 − 4 (1) (− 32) = 16 + 122 D > 0

Thus, the equation

x 2 − 4 x − 32 = 0

has two distinct real roots.
For option (4), the discriminant of the equation

3 x 2 + 43 x + 4 = 0.

Here,

a = 3, b = 43, c = 4.

D = b 2 − 4 a c = (43) 2 − 4 (3) (4) = 48 − 48 D = 0

Thus, the equation

3 x 2 + 43 x + 4 = 0

has equal real roots.
The equation

x 2 − 4 x + 32 = 0

has no real roots.
The correct option is (1).

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th