Kinda lost with this one
Given that
hx^3 - 12x^2 - x + 3=(2x-1) (2x+1) (x-k)
find the values of the constants k and h
don't even know where to start
when the sum of 1.9 and 2.2 is subtracted from the product of 1.9 and 2.2, what is the differance?
don't post ur stuff under my thing!!!!!!!!!!!!!!!!!!!
I apologize for the confusion caused by the previous unrelated comment. Let's focus on the first question you asked.
To find the values of the constants "k" and "h" in the equation hx^3 - 12x^2 - x + 3 = (2x-1) (2x+1) (x-k), you need to equate the corresponding terms on both sides of the equation.
Let's start by expanding the right side of the equation using the distributive property:
(2x-1) (2x+1) (x-k)
= (2x)(2x)(x) + (2x)(2x)(-k) + (2x)(-1)(x) + (2x)(-1)(-k) + (-1)(2x)(x) + (-1)(2x)(-k) + (-1)(-1)(x) + (-1)(-1)(-k)
Simplifying this expression, we get:
= 4x^3 - 4x^2k - 2x^2 + 2xk - 2x + 2xk - x + k
Now, let's compare the corresponding terms on both sides of the equation:
hx^3 - 12x^2 - x + 3 = 4x^3 - 4x^2k - 2x^2 + 2xk - 2x + 2xk - x + k
Comparing the coefficients of like terms, we get the following equations:
1) Coefficient of x^3 terms: h = 4
2) Coefficient of x^2 terms: -12 = -4k - 2
3) Coefficient of x terms: -1 = 2k - 2k - 1
4) Constant term: 3 = k
Solving these equations will give us the values of "k" and "h".
From equation 1, we have h = 4.
From equation 2, we can rewrite it as:
-12 = -4k - 2
-10 = -4k
k = -10/-4
k = 5/2 or 2.5
Therefore, the constant "k" is 2.5.
By substituting the value of "k" in equation 4, we have:
3 = k
3 = 2.5
Therefore, the constant "h" is 4 and the constant "k" is 2.5.
I hope this explanation helps you understand the steps involved in solving the given equation. Let me know if you need further clarification or have any other questions.