Question

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

Answer 1

It is given that the two roots of the polynomial are 2 and −5.
Let $\mathrm{\alpha }=2\mathrm{and}\mathrm{\beta }=-5$
Now, sum of the zeroes, $\mathrm{\alpha }+\mathrm{\beta }$ = 2 + (−5) = −3
Product of the zeroes, $\mathrm{\alpha \beta }$ = 2$\times$−5 = −10
∴ Required polynomial = $x^2-(\mathrm{\alpha }+\mathrm{\beta })x+\mathrm{\alpha \beta }$
$$\begin{gathered} =x^2—(-3)x+(-10) \\ =x^2+3x-10 \end{gathered}$$