Question

Find a quadratic polynomial whose zeroes are 2 and `-7/5`.

Answer 1

Given: The zeroes are 2 and `-7/5`.

Step-wise calculation:

1. Sum of zeroes = `2 + (-7/5) = 10/5 - 7/5 = 3/5`.

2. Product of zeroes = `2 xx (-7/5) = -14/5`.

3. A quadratic with roots α, β is x² – (α + β)x + αβ.

4. Substitute the values: `x^2 - (3/5)x - 14/5`.

5. Multiply by 5 to clear fractions: 5x² – 3x – 14.

A quadratic polynomial with the given zeroes is `x^2 - (3/5)x - 14/5` (monic). An integer-coefficient equivalent is 5x² – 3x – 14.