Question

If `2/3` and –3 are the zeros of the quadratic polynomial ax² + 7x + b then find the values of a and b.

Answer 1

Given: Zeros = `2/3` and –3 of the quadratic ax² + 7x + b.

Step-wise calculation:

1. Sum of zeros = `(2/3) + (-3)`

= `2/3 - 9/3`

= `-7/3`

But sum = `(-("Coefficient of"  x))/(("Coefficient of"  x^2)) = (-7)/a`.

So, `(-7)/3 = (-7)/a` 

⇒ `1/3 = 1/a`

⇒ a = 3

2. Product of zeros = `(2/3) xx (-3) = -2`.

Product = `(("Constant term"))/(("Coefficient of"  x^2)) = b/a`.

So, `b/a = -2` 

⇒ b = a(–2) = 3(–2)

⇒ b = –6