Question

Find the value of k, if 2x-3 is a factor of 2x^3-9x^2+x+k

Answer 1

$\huge\green {\underline {\mathfrak {Answer:}}}$

$\underline {\bold{\pink{Given:}}}$

➣$p(x)=2x^3 - 9x^2 + x + k$

➣$Factor = 2x-3$

$\underline {\bold{\pink {Find:}}}$

➣$k$

$\underline {\bold {\pink{Solution:}}}$

✦$\color{gold}{\mathcal{Putting \ p\left(\dfrac{3}{2} = 0\right)}}$

➫$p\left(\dfrac{3}{2}\right) = 0$

➫$2\left(\dfrac{3}{2}\right)^3 -9\left(\dfrac{3}{2}\right)^2 +\dfrac{3}{2} + k =0$

➫$2 \times \dfrac{27}{8} - 9 \times \dfrac{9}{4} + \dfrac{3}{2} + k = 0$

➫$\dfrac{27}{4} - \dfrac{81}{4} + \dfrac{3}{2} + k = 0$

➫$\dfrac{27-81+6}{4} + k = 0$

➫$\dfrac{-48}{4} + k = 0$

➫$k - 12 = 0$

$\color{cyan}{\boxed{\implies{\boxed{\color{red}{k = 12}}}}}$

Answer 2

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