Question

Find the value of K, if 2x – 3 is a factor of 2x3 - 9x2 + x + K.
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Answer 1

By using factor theorem, 

If 2x - 3 is 0, then x = 3/2

Now substitute the value of x in the equation

2x^3+kx^2+x + 12 = 0

2 (3/2)^3 + k (3/2)^2 + 3/2 + 12 = 0

54/8 + k(9/4) + 27/2 = 0

81/4 + k(9/4) = 0

k = -81/4

       9/4 

=9...

Answer 2

Step-by-step explanation:

f(x)=2x^3-9x^2+x+k

factor 2x-3=0

x=3/2

f(3/2)=0

$2( \frac{3}{2} ) ^{3} - 9( \frac{3}{2} ) ^{2} + x + k = 0$

$2( \frac{27}{8} ) - 9( \frac{9}{4} ) + \frac{3}{2} + k =$

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

$k = \frac{54}{4} - \frac{3}{2}$

$k = \frac{27 - 3}{2}$

$k = \frac{24}{2} = 12$