Question

find the zeroes of the quadratic polynomial 3x2-x-4 and verify the relationship between the zeroes and coefficient.

Answer 1

$<b ><i >$ Hey Mateyy!

Answer => In the attachment!

Answer 2

Answer:  Roots of quadratic polynomials are $\frac{4}{3},-1$

Step-by-step explanation:

Since we have given that

$3x^2-x-4$

First we will find the zeroes of the quadratic polynomial.

We will use "Split the middle terms":

$3x^2-x-4=0\\\\3x^2+3x-4x-4=0\\\\3x(x+1)-4(x+1)=0\\\\(3x-4)(x+1)=0\\\\x=\frac{4}{3},-1$

Now, Let, $\alpha =\frac{4}{3},\beta =-1$

Now, we will verify the relationship between the zeroes and coefficient.

Sum of zeroes is given by

$\alpha +\beta =\frac{4}{3}-1=\frac{1}{3}\\\\\alpha \beta =-1\times \frac{4}{3}=\frac{-4}{3}\\and\\\\\alpha +\beta =\frac{-b}{a}=\frac{1}{3},\alpha\beta =\frac{c}{a}=\frac{-4}{3}$

Hence, verified.

Roots of quadratic polynomials are $\frac{4}{3},-1$