Question

If (2x+1) is a factor of 6x³+5x²+ax-2
Find the value of a

Answer 1

Answer:

a= -3

Step-by-step explanation:

$(3x^{2} +x-2)(2x-1)$ = $6x^{3} +5x^{2}-3x-2$

Answer 2

$\huge{\underline{\underline{\bf{Solution}}}}$

$\rule{200}{2}$

$\tt given\begin{cases} \sf{Polynomial : 6x^3 + 5x^2 - ax - 2} \\ \sf{2x + 1 \: is \: a \: factor \: of \: polynomial.} \end{cases}$

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{To \: Find :}}}}$

We have to find the value of a.

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{Explanation :}}}}$

As, it is given (2x - 1) is a factor,

Then, A.T.Q

2x - 1 = 0

2x = 1

x = 1/2

$\rule{150}{2}$

Now, put value of x in polynomial

$\tt{6(\frac{1}{2})^3 + 5(\frac{1}{2})^2 - a(\frac{1}{2}) - 2 = 0} \\ \\ \tt{→\frac{6}{8} + \frac{5}{4} - \frac{1}{2}a - 2 = 0 } \\ \\ \tt{→\frac{6 + 10 - 4a - 16}{8} = 0} \\ \\ \tt{→16 - 16 = 4a} \\ \\ \tt{→a = 0}$

$\Large{\star{\boxed{\tt{a = 0}}}}$