Question

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

$6x^2-3-7x$

Answer 1

$6x^2-3-7x$
Comparing given polynomial with the general form $a{x}^2+bx+c$,
We get, a = 6, b = - 7 and c = -3
We have $6x^2-7x-3$ = $6x^2-9x+2x-3$
= 3x(2x - 3) +1(2x - 3)
= (3x + 1) (2x - 3)

The value of $6x^2-3-7x$ is 0 when 3x + 1 = 0 or 2x - 3 = 0,
i.e., $x=\frac{-1}{3}orx=\frac{3}{2}$

Therefore, the zeroes of $6x^2-3-7x$ are $\frac{-1}{3}and\frac{3}{2}$.

Sum of zeroes = $\frac{-1}{3}+\frac{3}{2}=\frac{7}{6}=-\frac{(-7)}{6}=\frac{-\left(Coefficientofx\right)}{Coefficientof{x}^2}$

Product of zeroes $=\frac{-1}{3}\times \frac{3}{2}=\frac{-1}{2}=\frac{-3}{6}=\frac{Constantterm}{Coefficientof{x}^2}$.