Find the value of m so that 2x - 1 be a factor of 8x⁴ + 4x³ - 16x² + 10x + m.
Solution:
Given, 2x - 1 is a factor of 8x⁴ + 4x³ - 16x² + 10x + m
We have to find the value of m.
Let the polynomial be p(x) = 8x⁴ + 4x³ - 16x² + 10x + m
Let the factor be g(x) = 2x - 1
Let g(x) = 0
2x - 1 = 0
2x = 1
x = 1/2
Substitute x = 1/2 in p(x),
Since g(x) is a factor of p(x), p(1/2) = 0
p(1/2) = 8x⁴ + 4x³ - 16x² + 10x + m = 0
8(1/2)⁴ + 4(1/2)³ - 16(1/2)² + 10(1/2) + m = 0
8/16 + 4/8 - 16/4 + 5 + m = 0
1/2 + 1/2 - 4 + 5 + m = 0
1 + 5 - 4 + m = 0
6 - 4 + m = 0
2 + m = 0
m = -2
Therefore, the value of m is -2.
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☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 21
Find the value of m so that 2x - 1 be a factor of 8x⁴ + 4x³ - 16x² + 10x + m
Summary:
The value of m so that 2x - 1 be a factor of 8x⁴ + 4x³ - 16x² + 10x + m is -2
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