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QUESTION:
For polynomials p(x) = 6x³ + 11x² + kx - 20 and q(x) = 9x² - 5x , x = 2 is a root of the polynomial (p(x) + q(x)). Then find the value of k.
ANSWER:
- The value of k = - 49
GIVEN:
- p(x) = 6x³ + 11x² + kx - 20
- q(x) = 9x ² - 5x
- x = 2 is a root of the polynomial (p(x) + q(x))
TO FIND:
- The value of k.
EXPLANATION:
p(x) + q(x) = 6x³ + 11x² + kx - 20 + 9x ² - 5x
p(x) + q(x) = 6x³ + 20x² + (k - 5)x - 20
x = 2 is a root of the polynomial p(x) + q(x).
p(2) + q(2) = 0
6(2³) + 20(2²) + (k - 5)2 - 20 = 0
6(8) + 20(4) + 2k - 10 - 20 = 0
48 + 80 + 2k - 30 = 0
2k + 80 + 18 = 0
2k + 98 = 0
k + 49 = 0
k = - 49
HENCE THE VALUE OF K = - 49
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