Question

The number of quadratic polynomials whose zeroes are 2 and – 3, is __________.

Answer 1

Quadratic polynomial with given zeroes is
x² – (sum of zeroes)x + (product of zeroes)

$$\begin{gathered} =x^2-\left(-3+2\right)x+\left(-3\times 2\right) \\ =x^2-\left(-1\right)x+\left(-6\right) \\ =x^2+x-6 \end{gathered}$$

Hence, the number of quadratic polynomials whose zeroes are 2 and – 3, is one.