Question

Find the values of a and b for which x = 3 / 4 and x = - 2 are the roots of the equation ax^2 + bx - 6 = 0.

Answer 1

If  α and β are the Roots of Quadratic Equation ax² + bx + c = 0 then :

Sum of the roots : α + β = -b/a

Product of the roots : α × β = c/a

Given Quadratic Equation : ax² + bx - 6 = 0

Comparing with Standard form we can see that :

a = a and b = b and c = -6

Given the Roots are 3/4 and -2

Let us take α = 3/4 and β = -2

⇒ Sum of the Roots : 3/4 - 2 = -b/a

⇒ -5/4 = -b/a

⇒ b/a = 5/4

Product of the Roots : 3/4 × (-2) = -6/a

⇒ -3/2 = -6/a

⇒ a = 4

substituting a = 4 in b/a = 5/4

⇒ b/4 = 5/4

⇒ b = 5

So the Value of a = 4 and Value of b = 5

The Given Quadratic Equation becomes : 4x² + 5x - 6 = 0