Question

Find a quadratic polynomial whose zeros are 2 and –5.

Answer 1

Given: The zeros are 2 and –5.

Step-wise calculation:

1. Sum of zeros S = 2 + (–5) = –3.

2. Product of zeros P = 2 × (–5) = –10.

3. A quadratic with zeros α and β has the form k(x² – (α + β)x + αβ). Choose k = 1 for the monic polynomial.

4. Substitute S and P:

x² – (–3)x + (–10) = x² + 3x – 10

Also (x – 2)(x + 5) = x² + 3x – 10

One quadratic polynomial with the given zeros is x² + 3x – 10.