for what value of a the polynomial 2 x ki power 3 e plus 2 x square + 11 x + a + 3
Answers
Answer:
Dear Student,
Answer: a = -7
Solution:
from polynomial 2x-1
put the value of x,in cubic polynomial,and solve for a.
\begin{gathered}2x - 1 = 0 \\ \\ 2x = 1 \\ \\ x = \frac{1}{2} \end{gathered}
2x−1=0
2x=1
x=
2
1
if given polynomial is exactly divisible by 2x-1, than on putting x = 1/2, it becomes zero.
\begin{gathered}2 {x}^{3} + a {x}^{2} + 11x + a + 3 \\ \\ 2( { \frac{1}{2}) }^{3} + a( { \frac{1}{2} )}^{2} + 11( \frac{1}{2} ) + a + 3 = 0 \\ \\ 2 \times \frac{1}{8} + a \times \frac{1}{4} + \frac{11}{2} + a + 3 = 0 \\ \frac{1}{4} + \frac{a}{4} + \frac{11}{2} + a + 3 = 0 \\ \frac{a}{4} + a = - 3 - \frac{11}{2} - \frac{1}{4} \\ \\ \frac{a + 4a}{4} = \frac{ - 12 - 22 - 1}{4} \\ \\ 5a = - 35 \\ \\ a = \frac{ - 35}{5} \\ \\ a = - 7\end{gathered}
2x
3
+ax
2
+11x+a+3
2(
2
1
)
3
+a(
2
1
)
2
+11(
2
1
)+a+3=0
2×
8
1
+a×
4
1
+
2
11
+a+3=0
4
1
+
4
a
+
2
11
+a+3=0
4
a
+a=−3−
2
11
−
4
1
4
a+4a
=
4
−12−22−1
5a=−35
a=
5
−35
a=−7
The value of a = -7.
Hope it helps you.