Question

Find the value of m so that 2x – 1 be a factor of 8x4 + 4x3 – 16 x2 + 10x + m
Head Office Address: 2nd & 3rd Floor, STC, Near ISBT, Hamirpur (HP) - 177001 answer is -2 ​

Answer 1

Answer :

m = -2

Step-by-step explanation :

Given,

(2x - 1) is a factor of 8x⁴ + 4x³ - 16x² + 10x + m

To find,

The value of m = ?

Solution,

Let p(x) = 8x⁴ + 4x³ - 16x² + 10x + m

➟ (2x - 1) is a factor

       2x - 1 = 0

       2x = 0 + 1

       2x = 1

         x = 1/2

➣ Since (2x - 1) is a factor, when we substitute x = 1/2, it doesn't leave any remainder. i.e., the result is zero.

               p(1/2) = 0

     ➟  8x⁴ + 4x³ - 16x² + 10x + m  =  0

       

       $\bf \Longrightarrow \ \ 8(\frac{1}{2})^4+4(\frac{1}{2})^3-16(\frac{1}{2})^2+10(\frac{1}{2})+m=0 \\\\ \Longrightarrow \ \ 8(\frac{1}{16})+4(\frac{1}{8})-16(\frac{1}{4})+10(\frac{1}{2})+m=0 \\\\ \Longrightarrow \ \ \frac{8}{16}+\frac{4}{8}-\frac{16}{4}+\frac{10}{2}+m=0\\\\ \Longrightarrow \ \ \frac{1}{2} +\frac{1}{2}-4+5+m=0\\\\ \Longrightarrow \ \ \frac{1+1}{2}+1+m=0\\\\ \Longrightarrow \ \ \frac{2}{2}+1+m=0 \\\\ \Longrightarrow \ \ 1+1+m=0 \\\\ \Longrightarrow \ \ 2+m=0 \\\\ \Longrightarrow \ \ m=-2$

The value of m is -2

Answer 2

Step-by-step explanation:

Let p(x) = 8x⁴ + 4x³ - 16x² + 10x + m

➟ (2x - 1) is a factor

2x - 1 = 0

2x = 0 + 1

2x = 1

x = 1/2

➣ Since (2x - 1) is a factor, when we substitute x = 1/2, it doesn't leave any remainder. i.e., the result is zero.

p(1/2) = 0

➟ 8x⁴ + 4x³ - 16x² + 10x + m = 0