Question

if the roots of 4x square + 6x + 1 = 0 are equal then find possible values of b

Answer 1

Answer:

[5,9]

Step-by-step explanation:

Given quadratic equation is

x

2

+6x+b=0

Since, roots are real and distinct i.e. D>0

⇒36−4b>0

⇒b<9

Also, (α−β)

2

=(α+β)

2

−4αβ

(α−β)

2

=36−4b

Given, α−β≤4

⇒(α−β)

2

≤16

36−4b≤16

⇒b≥5

Hence, range of b is [5,9).