Question

Find the sum and product of the zeroes of the following quadratic polynomials.

$x^2-2bx-15b^2$

Answer 1

The standard form of any polynomial is $\left(\mathrm{coefficient}\mathrm{of}{x}^2\right)x^2+\left(\mathrm{coefficient}\mathrm{of}x\right)x+\mathrm{constant}\mathrm{term}$.

Here, coefficient of $x^2$ is $1$, coefficient of $x$ is $-2b$, and constant term is $-15b^2$.

Step 1: To find the sum of zeroes.

Sum of zeroes = $\frac{-\left(\mathrm{coefficient}\mathrm{of}x\right)}{\mathrm{coefficient}\mathrm{of}{x}^2}=\frac{-\left(-2b\right)}{1}=2b$

Step 2: To find the product of zeroes.

Product of zeroes = $\frac{\mathrm{constant}\mathrm{term}}{\mathrm{coefficient}\mathrm{of}{x}^2}=\frac{-15b^2}{1}=-15b^2$

Hence, the sum and product of zeroes are $2b\mathrm{and}-15b^2$ respectively.