CBSE · Class 10 · Mathematics · PolynomialsWrite the quadratic polynomial whose sum and product of zeroes are $-3$ and $2$ respectively.

If the sum of zeroes $(\alpha + \beta)$ and the product of zeroes $(\alpha \beta)$ of a quadratic polynomial are given, the general quadratic polynomial can be expressed using the formula $P(x) = k[x^2 - (\text{sum of zeroes})x + (\text{product of zeroes})]$, where $k$ is a non-zero real constant. Substituting the given values, sum $= -3$ and product $= 2$, we get $P(x) = k[x^2 - (-3)x + 2] = k[x^2 + 3x + 2]$. For $k = 1$, the required quadratic polynomial is $x^2 + 3x + 2$.