Question

If the roots of the quadratic equation x2 + 6x + b = 0 are real and distinct and they differ by atmost 4 then the least
value of b is-
(A) 5
(B) 6
(C) 7
(D) 8​

Answer 1

Answer:

5,9

Step-by-step explanation:

Given quadratic equation is x2+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).