Question

Let a , b ∈ R be such that the equation ax 2 – 2 bx + 15 = 0 has a repeated root α. If α and β are the roots of the equation x 2 – 2 bx + 21 = 0, then α2 + β2 is equal to

• A. 37
• B. 58
• C. 68
• D. 92

Answer 1

Answer: (A)

37

Answer 2

The correct option is(B): 58.

ax 2 – 2 bx + 15 = 0 has repeated root so b 2 = 15 a

and

$α=\frac{15}{b}$

∵α is a root of x 2 – 2 bx + 21 = 0

So

$\frac{225}{b^2}=9⇒b^2=25$

Now α2 + β2 = (α + β)2 – 2αβ = 4 b 2 – 42 = 100 – 42

= 58