Is it true that every quadratic equation has at least two 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

True

False

answer is B.

(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

Given statement is that every quadratic equation has at least two real roots.
A quadratic equation can have

0, 1

2

roots at a time.
Thus, the minimum number of roots of a quadratic equation is

0

.
For example, a quadratic equation,

x 2 − 4 x + 4 = 0

has only one root which is

2

.
That is for some quadratic equations, there exist only one real root.
And for the quadratic equation,

x 2 + 4 x + 10 = 0

has no real root.
So we can conclude that the given statement is false.
The correct statement is, for some quadratic equations, there exist no roots.
Hence, the correct option is 2.

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 Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

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 Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE