NCERT · Class 10 · Mathematics · PolynomialsHow can you form a quadratic polynomial if the sum and product of its zeros are given as $S$ and $P$ respectively?

To form a quadratic polynomial when the sum of the zeros ($S = \alpha + \beta$) and the product of the zeros ($P = \alpha \beta$) are known, we use the standard construction formula. The polynomial can be written as $k[x^2 - (\text{sum of zeros})x + (\text{product of zeros})]$, which simplifies to $k[x^2 - Sx + P]$, where $k$ is any non-zero real constant. In most textbook problems, we assume $k = 1$ for simplicity, resulting in the polynomial $x^2 - Sx + P$. This method is highly efficient as it allows us to find the quadratic expression directly without needing to calculate the individual values of the zeros first.