Question

Question 1 (vi)
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

$3x^2-x-4$

Answer 1

$3x^2-x-4$
Comparing given polynomial with the general form $a{x}^2+bx+c$,
We get a = 3, b = -1 and c = -4
We have $3x^2-x-4$ = $3x^2-4x+3x-4$
= x(3x - 4)+1(3x - 4) = (x + 1) (3x - 4)
The value of $3x^2-x-4$ is 0 when 3x - 4 = 0 and x + 1 = 0,i.e., when x = $\frac{4}{3}$ or x = -1
Therefore, the zeroes of $3x^2-x-4$ are $\frac{4}{3}$ and -1.
Sum of zeroes = $\frac{4}{3}$ + (-1) = $\frac{1}{3}$ = $\frac{-(-1)}{3}=\frac{-\left(Coefficientofx\right)}{Coefficientof{x}^2}$
Product of zeroes = $\frac{4}{3}\times (-1)=\frac{-4}{3}=\frac{Constantterm}{Coefficientof{x}^2}$