Dtermine the value of K such that -2 is cone root of the equation 2x^3+(K+1)x^2=4-x^2
I tried it a couple of times and I keep getting the wrong answer. The answer is K=3.
If x = -2 is a root, then
2(-2)^3 + (k+1)(-2)^2 = 4 - (-2)^2
-16 + (k+1)(4) = 4 - 4
4(k+1) = 16
k+1 = 4
k = 3
the most likely error you made probably is in the
(-2)^3 = -8
or
- (-2)^2
= -(4)
= -4
To determine the value of K such that -2 is a root of the equation 2x^3 + (K+1)x^2 = 4 - x^2, we can follow these steps:
Step 1: Plug -2 into the equation.
Replace each occurrence of x in the equation with -2:
2(-2)^3 + (K+1)(-2)^2 = 4 - (-2)^2
Simplifying, we get:
2(-8) + (K+1)(4) = 4 - 4
-16 + 4K + 4 = 0
Step 2: Simplify the equation.
Combining like terms, we have:
4K - 12 = 0
Step 3: Isolate K.
Adding 12 to both sides, we get:
4K = 12
Dividing both sides by 4, we find:
K = 3
Therefore, the value of K that satisfies the given equation is K = 3, as you mentioned.
To determine the value of K such that -2 is a root of the equation 2x^3 + (K + 1)x^2 = 4 - x^2, we need to use the fact that if -2 is a root, then substituting x = -2 into the equation should make the equation true.
Let's start by substituting x = -2 into the equation:
2(-2)^3 + (K + 1)(-2)^2 = 4 - (-2)^2
Simplifying this expression, we get:
2(-8) + (K + 1)(4) = 4 - 4
-16 + 4K + 4 = 0
Combine like terms:
4K - 12 = 0
Add 12 to both sides:
4K = 12
Divide both sides by 4:
K = 3
So, the value of K that makes -2 a root of the equation is K = 3.
If you got a different answer when you solved it, there may have been an error in your calculations. Make sure to double-check your arithmetic.