find the zeros,the sum of the zeros and the product of the zeros of the quadratic polynomial p(x)=3x square-x-4
Answers
Step-by-step explanation:
In the given polynomial 3x
2
−x−4,
The first term is 3x
2
and its coefficient is 3.
The middle term is −x and its coefficient is −1.
The last term is a constant term −4.
Multiply the coefficient of the first term by the constant 3×−4=−12.
We now find the factor of 12 whose sum equals the coefficient of the middle term, which is −1 and then factorize the polynomial 3x
2
−x−4 and equate it to 0 as shown below:
3x
2
−x−4=0
⇒3x
2
+3x−4x−4=0
⇒3x(x+1)−4(x+1)=0
⇒(x+1)(3x−4)=0
⇒(x+1)=0,(3x−4)=0
⇒x=−1,3x=4
⇒x=−1,x=
3
4
Therefore, the zeroes of the polynomial 3x
2
−x−4 are −1,
3
4
.
Now, the sum and the product of the zeroes of the given quadratic polynomial is as follows:
−1+
3
4
=
3
−3+4
=
3
1
−1×
3
4
=−
3
4
Hence, the sum of the zeroes is
3
1
and the product of the zeroes is −
3
4
.