if (2x+1) is a factor of 6x^3+5x^2+ax-2 , find the value of a.
Answers
Answer:
(x) = 6x³+5x²+ax-2
g(x) = 2x+1
To find =》
value of a
Solution =》
p(x) =6x³+5x²+ax-2
g(x) = 2x+1=0
2x=-1
x=-1/2
putting value of x in p(x)
6x³+5x²+ax-2=0
\begin{gathered}6 \times ( \frac{ - 1}{2} ) {}^{3} + 5 \times ( \frac{ - 1}{2} ) {}^{2} + a \times ( \frac{ - 1}{2} ) - 2 = 0 \\ = 6 \times ( \frac{ - 1}{8} ) + 5 \times ( \frac{ - 1}{4} ) + a \times ( \frac{ - 1}{2} ) - 2 = 0 \\ = \frac{ - 6}{8} + \frac{5}{4} - \frac{a}{2} - \frac{2}{1} = 0 \\ = \frac{ - 6 + 10 - 4a - 16}{8} = 0 \\ = - 6 + 10 - 4a - 16 = 0 \\ = - 22 + 10 - 4a = 0 \\ = - 12 - 4a = 0 \\ = - 4a = 12 \\ = a = \frac{ - 12}{4} \\ = a = - 3\end{gathered}
6×(
2
−1
)
3
+5×(
2
−1
)
2
+a×(
2
−1
)−2=0
=6×(
8
−1
)+5×(
4
−1
)+a×(
2
−1
)−2=0
=
8
−6
+
4
5
−
2
a
−
1
2
=0
=
8
−6+10−4a−16
=0
=−6+10−4a−16=0
=−22+10−4a=0
=−12−4a=0
=−4a=12
=a=
4
−12
=a=−3
Value of a is -3
Answer:
Given =》
p(x) = 6x³+5x²+ax-2
g(x) = 2x+1
To find =》
value of a
Solution =》
p(x) =6x³+5x²+ax-2
g(x) = 2x+1=0
2x=-1
x=-1/2
putting value of x in p(x)
6x³+5x²+ax-2=0
\begin{gathered}6 \times ( \frac{ - 1}{2} ) {}^{3} + 5 \times ( \frac{ - 1}{2} ) {}^{2} + a \times ( \frac{ - 1}{2} ) - 2 = 0 \\ = 6 \times ( \frac{ - 1}{8} ) + 5 \times ( \frac{ - 1}{4} ) + a \times ( \frac{ - 1}{2} ) - 2 = 0 \\ = \frac{ - 6}{8} + \frac{5}{4} - \frac{a}{2} - \frac{2}{1} = 0 \\ = \frac{ - 6 + 10 - 4a - 16}{8} = 0 \\ = - 6 + 10 - 4a - 16 = 0 \\ = - 22 + 10 - 4a = 0 \\ = - 12 - 4a = 0 \\ = - 4a = 12 \\ = a = \frac{ - 12}{4} \\ = a = - 3\end{gathered}
6×(
2
−1
)
3
+5×(
2
−1
)
2
+a×(
2
−1
)−2=0
=6×(
8
−1
)+5×(
4
−1
)+a×(
2
−1
)−2=0
=
8
−6
+
4
5
−
2
a
−
1
2
=0
=
8
−6+10−4a−16
=0
=−6+10−4a−16=0
=−22+10−4a=0
=−12−4a=0
=−4a=12
=a=
4
−12
=a=−3