If x + 1 is a factor of the polynomial 2x² + kx, then the value of k is
a. -3
b. 4
c. 2
d. -2
Solution:
Consider p(x) = 2x² + kx
As x + 1 is a factor of p(x)
p(-1) = 0
Substituting x = - 1
2(-1)² + k(-1) = 0
By further calculation
2 - k = 0
k = 2
Therefore, the value of k is 2.
✦ Try This: If x + 2 is a factor of the polynomial 3x² + kx, then the value of k is
Consider p(x) = 3x² + kx
As x + 2 is a factor of p(x)
p(-2) = 0
Substituting x = - 2
3(-2)² + k(-2) = 0
By further calculation
12 - 2k = 0
2k = 12
Dividing both sides by 2
k = 6
Therefore, the value of k is 6.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.1 Problem 12
If x + 1 is a factor of the polynomial 2x² + kx, then the value of k is a. -3, b. 4, c. 2, d. -2
Summary:
The process of factoring polynomials involves expressing the polynomial as the product of its factors. If x + 1 is a factor of the polynomial 2x² + kx, then the value of k is 2
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