Question

Find the zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:

5x² + 10x

Answer 1

Given: Polynomial: 5x² + 10x (so a = 5, b = 10, c = 0)

Step-wise calculation:

1. Factor: 5x² + 10x = 5x(x + 2).

2. Set equal to zero: 5x(x + 2) = 0

⇒ 5x = 0 or x + 2 = 0

3. Zeros: x = 0 and x = –2.

4. Sum of zeros: 0 + (–2) = –2.

5. Product of zeros: 0 × (–2) = 0.

6. Verify with coefficients:

For ax² + bx + c, sum = `-b/a` and product = `c/a`

Here `-b/a = -10/5 = -2` and `c/a = 0/5 = 0`, which match the computed sum and product.

The zeros are x = 0 and x = –2. The sum and product of the zeros equal `-b/a` and `c/a` respectively, so the relationship between zeros and coefficients is verified.