Question

If 2x – 1 and x + 2 are the factors of 2x^3 – ax^2 – 8x + b, then find the values of a and b.

Answer 1

Step-by-step explanation:

hope this helps you and look the answer once

Answer 2

Answer:

 $\frac{15}{68} and \frac{-15}{17}$ is the required value of a and b

Step-by-step explanation:

Explanation:

Given , 2x-1 and x+ 2 are the factor of $2x^{3} -ax^{2} -8x+b$

Let $P(x) = 2x^{3} -ax^{2} -8x+b$  

Now , given two factors (2x-1) and 9x+2)

Step1:

Therefore, we have 2x-1  

⇒x= $\frac{1}{2}$

Now , P($\frac{1}{2}$) = $2(\frac{1}{2}) ^{3} -a(\frac{1}{2} )^{2} -8(\frac{1}{2} )+b$

⇒P($\frac{1}{2}$) = $2(\frac{1}{8}) -a(\frac{1}{4} ) -8(\frac{1}{2} )+b$

        = $(\frac{1}{4}) -a(\frac{1}{4} ) -4+b$

       = $\frac{1-a-16+4b}{4}$ = 0

       = -a+4b -15= 0

⇒ P($\frac{1}{2}$)   =   -a+4b = 15        ......(i)

Step2:

Now , for x+2 . so , the value of x is -2

Put value of x = -2 in the equation .

P(-2) = $2(-2)^{3} -a(-2)^{2} -8(-2)+b$

         = 2 (-8) -a (4) +16 +b

         = -16 -4a +b +16

         = -4a +b = 0 ..........(ii)

Step3:

Now , from equation (i) and (ii)

-a +4b = 15 and

-4a + b = 0

On solving this equation , we get     b = $\frac{-15}{17}$

Now , put the value of b = $\frac{-15}{17}$ in any one of this equation we get ,

-4×(a) + $\frac{-15}{17}$ = 0

⇒a = $\frac{15}{68}$

Final answer :

Hence , the  value of a and b is  $\frac{15}{68} and \frac{-15}{17}$