Question

Find the quadratic polynomial, the sum of whose zeros is –5 and their product is 6.

Answer 1

Given: Sum of zeros = –5, Product of zeros = 6.

Step-wise calculation:

1. Let the zeros be α and β.

Then α + β = –5 and αβ = 6.

2. A quadratic (monic) with sum S and product P of zeros is x² – Sx + P; taking S = α + β and P = αβ gives x² – (α + β)x + αβ.

3. Substitute α + β = –5 and αβ = 6:

x² – (–5)x + 6 = x² + 5x + 6

4. Verify by factoring:

x² + 5x + 6 = (x + 2)(x + 3)

zeros –2 and –3 (sum –5, product 6)

The required quadratic polynomial is x² + 5x + 6.