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(x³+kx²-3)(x-2)=+7x³-18x²-3x+6
In the equation above, k is a constant. If the equation is true for all values of x, what is the value of k?
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Given : (x³ + kx² - 3)(x - 2) = x⁴ + 7x³ - 18x² - 3x + 6
To find : value of k if the equation is true for all values of x
Solution:
(x³ + kx² - 3)(x - 2) = x⁴ + 7x³ - 18x² - 3x + 6
=> x⁴ + kx³ - 3x -2x³ - 2kx² + 6 = x⁴ + 7x³ - 18x² - 3x + 6
=> x³(k - 2 - 7) + x²(-2k + 18) = 0
=> x³(k - 9) -2x²(k - 9) = 0
=> (x³ - 2x²)(k - 9) = 0
equation is true for all values of x
=> k - 9 =0
=> k = 9
value of k = 9
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