Question

85 Find the zero of following quadratic polynomial
and verify the relationships between zeroes and the
coefficient
ii) 3x²-x-4​

Answer 1

Answer:

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

3

4

,−1

Step-by-step explanation:

Since we have given that

3x^2-x-43x

2

−x−4

First we will find the zeroes of the quadratic polynomial.

We will use "Split the middle terms":

\begin{lgathered}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\end{lgathered}

3x

2

−x−4=0

3x

2

+3x−4x−4=0

3x(x+1)−4(x+1)=0

(3x−4)(x+1)=0

x=

3

4

,−1

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

3

4

,β=−1

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

Sum of zeroes is given by

\begin{lgathered}\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}\end{lgathered}

α+β=

3

4

−1=

3

1

αβ=−1×

3

4

=

3

−4

and

α+β=

a

−b

=

3

1

,αβ=

a

c

=

3

−4

Hence, verified.

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

3

4

,−1

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