Question

A quadratic equation with integral coeff. has two different prime numbers as its roots if the sum of the coefficients of the equation is prime then the sum of the roots is

• A. 2
• B. 5
• C. 7
• D. 11

Answer 1

Answer: (B)

5

Answer 2

Let equation is K (x – α) (x– β) = 0 where α, β are prime nos.

Sum of coeffs.

= K – K(α + β) + Kαβ = K (α – 1) (β – 1)

Prime

⇒ K = 1 & one of (α – 1) & (β – 1) will be one

let α – 1 = 1 ⇒ α = 2

β–1 will be 2

So β = 3

Hence sum of roots = 5