Question

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

($x^2-9x+14$)

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 $-9$, and constant term is $14$.

Step 1: To find the sum of zeroes:

Sum of zeroes = $\frac{-\left(\mathrm{coefficient}\mathrm{of}x\right)}{\mathrm{coefficient}\mathrm{of}{x}^2}=\frac{-\left(-9\right)}{1}=9$

Step 2: To find the product of zeroes:

Product of zeroes = $\frac{\mathrm{constant}\mathrm{term}}{\mathrm{coefficient}\mathrm{of}{x}^2}=\frac{14}{1}=14$

Hence, the sum and product of zeroes are $9and14$ respectively.