Question

If the zeroes of the quadratic polynomial x² + (a + 1)x + b are 2 and –3, then find the values of a and b.

Answer 1

Given: The zeroes of the quadratic polynomial x² + (a + 1)x + b are 2 and –3.

Step 1: Use the sum of zeroes formula:

For a quadratic polynomial x² + px + q:

α + β = −p

Here, α = 2, β = −3

So, 2 + (−3) = −1

According to the formula:

−(a + 1) = −1

a + 1 = 1

a = 0

Step 2: Use the product of zeroes formula:

αβ = q

2 × (−3) = −6

So, b = −6

Hence, a = 0 and b = –6.