Question

One of the roots of the equation is double of one of the roots of the equation. If m ? 0, then find its value. Select one:

Answer 1

mujhe nahi aata bhi kise aur se puch le

Answer 2

Let the roots of the quadratic equation x2 – 3x + 2m=0 be 2α and β Hence sum of roots (2α + β) = 3/1 ⇒ 2α + β = 3  → (1) Product of roots (2αβ) = 2m/1 ⇒ αβ = m  → (2) Let the roots of x2 –x + m = 0 be α and ɣ Hence sum of roots ( α + ɣ) = 1/1 ⇒ α + ɣ =  1  → (3) Product of roots (αɣ) = m/1 ⇒ αɣ = m  → (4) From equations (3) and (4), we get αβ = αɣ Thus β = ɣ Now equation (3) becomes, α + β = 1  → (5) Subtract (5) from (1), we get 2α + β = 3  α + β = 1  ---------------- α = 2 Hence β = - 1 But m = αβ from (2) Therefore m = 2(-1) = - 2