If ax2+bx+1=0, a∈R,b∈R, does not have distinct real roots, then the maximum value of b2is

A
$- 4 a$
B
$4 a$
C
$2 a$
D
$- 2 a$

Solution:

It is given that

a x^{2} + bx + 1 = 0, a \in R, b \in R,

does not have distinct real roots.
Discriminant is given by

D = b^{2} - 4 ac

.
Here are the relations between roots and discriminant
●       When roots are non-real, the discriminant is less than 0
●       When roots are real and equal, the discriminant is equal to 0
●       When the roots real and unequal the discriminant is greater than 0
The equation

a x^{2} - bx + 1 = 0

has no distinct real roots
This implies

D = b^{2} - 4 ac \leq 0

{= b}^{2} - 4 a \leq 0

= b² \leq 4 a

Hence, the correct option is 2.

If $a x^{2} + bx + 1 = 0, a \in R, b \in R,$ does not have distinct real roots, then the maximum value of $b^{2}$ is

Solution:

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