find the zeros of p(x) = 4x²-256 and also find sum and the product of the zeros of the polynomial
Answers
Answer:
In the given polynomial 4x
2
+12x+5,
The first term is 4x
2
and its coefficient is 4.
The middle term is 12x and its coefficient is 12.
The last term is a constant term 5.
Multiply the coefficient of the first term by the constant 4×5=20.
We now find the factor of 20 whose sum equals the coefficient of the middle term, which is 12 and then factorize the polynomial 4x
2
+12x+5 and equate it to 0 as shown below:
4x
2
+12x+5=0
⇒4x
2
+2x+10x+5=0
⇒2x(2x+1)+5(2x+1)=0
⇒(2x+1)(2x+5)=0
⇒2x=−1,2x=−5
⇒x=−
2
1
,x=−
2
5
Therefore, the zeroes of the polynomial 4x
2
+12x+5 are −1,
3
4
.
Now, the sum and the product of the zeroes of the given quadratic polynomial is as follows:
−
2
1
+(−
2
5
)=−
2
1
−
2
5
=−
2
6
=−3
(−
2
1
)×(−
2
5
)=
2
1
×
2
5
=
4
5
Hence, the sum of the zeroes is −3 and the product of the zeroes is
4
5
.
Answer:
5/4 is your answer hope it is helpful