Math, asked by tojatih192, 9 months ago

I would mark the brainliest to the first answer
(x³+kx²-3)(x-2)=x^{4}+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?

Answers

Answered by amitnrw
0

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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