Question

If a and b are the roots of the quadratic equation x^2 - 5x + 3(k-1) = 0 are such that a-b =11. Find 'k'

Answer 1

If  α and β are the roots of Quadratic Equation px² + qx + r = 0 then :

Sum of the roots : α + β = -q/p

Product of the roots : α × β = r/p

Given Quadratic Equation is x² - 5x + 3(k - 1) = 0 and its roots are 'a' and 'b'

By comparing with the above, we can say that p = 1 and q = -5 and r = 3(k - 1) and α = a and β = b

⇒ Sum of the roots : a + b = 5

⇒ Product of the roots : a × b = 3(k - 1)

it is also given that a - b = 11

Adding a + b = 5 and a - b = 11 we get :

⇒ 2a = 16

⇒ a = 8 and b = -3

Product of the roots : a × b = 3(k - 1)

⇒ 8 × -3 = 3k - 3

⇒ -24 = 3k - 3

⇒ 3k = -21

⇒ k = -7