Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
2.0k views
in Quadratic Equations by (31.2k points)
closed by

Is there any real value of 'a' for which the equation 

x2 + 2x + (a2 + 1) = 0 has real roots?

1 Answer

+1 vote
by (30.8k points)
selected by
 
Best answer

A quadratic equation has two real roots if discriminant = 0 

For the given equation, we have: 

d = b2 – 4 a c 

d = (2)2 – 4 (1) (a2 + 1) 

d = 4 – 4(a2 + 1) 

d = 4(1 – a2 – 1) 

d = – 4a2

Now, D = 0 when a = 0. So, the equation will have real and equal roots if a = 0. And for all other values of a, the equation will have no real roots.

No, there is no real value of ‘a’ for which the given equation has real roots.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...