Question

p(x) = ax^2 + 7x + b. If the zeroes are 2/3 and -3, can the values of a & b be 3 & -1 respectively.

Answer 1

The Zeroes of a Quadratic Polynomial are the Roots of the Quadratic Equation.

Given that 2/3 and -3 are the Zeroes of the Quadratic Polynomial ax² + 7x + b

⇒ 2/3 and -3 are the Roots of the Quadratic Equation ax² + 7x + b = 0

⇒ Sum of the Roots = 2/3 - 3 = -7/a

⇒ -7/3 = -7/a

⇒ a = 3

Product of the Roots = 2/3 × -3 = b/a

⇒ -2 = b/a

but we found that a = 3

⇒ b = -6

So the Values of 'a' and 'b' are 3 and -6