find the zeros of given quadratic polynomial and verify the relatoinship between the zeros and cofficent x
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Let f(x)=3x
2
−x−4
To calculate the zeros of the given equation, put f(x)=0.
3x
2
−x−4=0
3x
2
−4x+3x−4=0
x(3x−4)+1(3x−4)=0
(x+1)(3x−4)=0
x=−1,x=
3
4
The zeros of the given equation is −1 and
3
4
.
Sum of the zeros is −1+
3
4
=
3
1
.
Product of the zeros is −1×
3
4
=−
3
4
.
According to the given equation,
The sum of the zeros is,
a
−b
=
3
−(−1)
=
3
1
The product of the zeros is,
a
c
=
3
−4
Hence, it is verified that,
sumofzeros=
coefficientofx
2
−coefficientofx
And,
productofzeros=
coefficientofx
2
constantterm
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