Question

Find the zeroes of the polynomial 3x2–27 and verify the relationship between the zeroes and
the co-efficients.​

Answer 1

Step-by-step explanation:

Given that,

A polynomial, 3x^2-273x

2

−27

To find,

Zeros.

Solution,

Let the given polynomial is f(x) such that,

f(x)=3x^2-27f(x)=3x

2

−27

To find the zeroes of the given polynomial,

Put f(x) = 0

\begin{gathered}3x^2=27\\\\x^2=9\\\\x=\pm 3\end{gathered}

3x

2

=27

x

2

=9

x=±3

Zeroes are +3 and -3.

Sum of zeroes, =\dfrac{-b}{a}=

a

−b

In the given equation, a = 3, b = 0 and c = -27

Sum of zeroes, =\dfrac{-b}{a}=-3+3=0=

a

−b

=−3+3=0

The product of zeroes,

\begin{gathered}=\dfrac{c}{a}\\\\-3\times 3=\dfrac{-27}{3}\\\\-9=-9\end{gathered}

=

a

c

−3×3=

3

−27

−9=−9

Hence, this is the required solution.