If the difference between the roots of the equation Ax2 – Bx + C = 0 is 4, then which of the following is TRUE?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. B2 – 10A2 = 4AC + 6A2
Ax2 – Bx + C = 0
Roots of the equation are α, β
α + β = B/A .....(1)
αβ = C/A .....(2)
α - β = 4 .....(3)
α + β = B/A .....(4)
from equation (3) and (4)
2α = B/A + 4
α = B/2A + 2
β = B/2A - 2
By putting in equation (2)
αβ = C/A
(B/2A)2 - 4 × C/A
B2/4A2 - 4 = C/A
B2 – 10A2 = 4AC + 6A2