Question

If (2t+1) is the factor of the polynomial p(t)=4t^3 + 4t^2 -t-1,then the value of p(-1/2) is:

With Full Explanation!!​

Answer 1

4x
2
+5
2
​
x−3
=4x
2
+6
2
​
x−
2
​
x−3
=2
2
​
x(
2
​
x+3)−(
2
​
x+3)
=(
2
​
x+3)(2
2
​
x−1)
So, the zeros of the polynomial are
(
2
​
x+3)=0 and (2
2
​
x−1)=0
x=
2
​

−3
​
and x=
2
2
​

1
​

x=
2
−3
2
​

​
and x=
4
2
​

​

Now, the polynomial is 4x
2
+5
2
​
x−3
Comparing it with ax
2
+bx+c=0, we get a=4, b=5
2
​
and c=−3
Sum of the zeros =
2
−3
2
​

​
+
4
2
​

​

=
4
−6
2
​
+
2
​

​

=
4
−5
2
​

​

=
a
−b
​

Product of the zeros =(
2
−3
2
​

​
)(
4
2
​

​
)
=(
2
−3
​
)(
4
2
​
)
=
4
−3
​

=
a
c
​