Find the value of k, if 2 is a zero of the polynomial 2x⁴ + x³ + kx² - 8?
- -5
- -6
- -8
- None of these
Explanation
Given 2 is a zero of the polynomial 2x⁴ + x³ + kx² - 8, we substitute x = 2 into the polynomial and set it equal to 0:
2(2)⁴ + (2)³ + k(2)² - 8 = 0
2(16) + 8 + 4k - 8 = 0
32 + 8 + 4k - 8 = 0
32 + 4k = 0
Now, solve for k:
4k = -32
k = -32/4
k = -8
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