Question

Find the zeros of the quadratic polynomial 6x² - 13x + 6 and verify the relation between the zero and its coefficients.

Answer 1

We have, 6x² -13x + 6 = 6 x 2 - 4x - 9x + 6

= 2x(3x - 2) - 3(3x -2)

= (3x - 2) (2x - 3)

So, the value of 6x² - 13x + 6 is 0 when

(3x - 2) = 0 or (2x - 3) = 0 i.e.,

When x = ${\displaystyle \frac{2}{3}}$ or ${\displaystyle \frac{3}{2}}$

Sum of the zeros

=${\displaystyle \frac{2}{3}+\frac{3}{2}=\frac{13}{6}=-\frac{(-13)}{6}=-\left[\frac{\text{coefficient of x}}{\text{coefficient of}{x}^2}\right]}$

Product of the zeros 

=${\displaystyle \frac{2}{3}\times \frac{3}{2}=\frac{6}{6}=\left[\frac{\text{coefficient of x}}{\text{coefficient of}{x}^2}\right]}$