A: Solve the following equation:
k2 + 4k = 0
A: By factoring
B: By using the quadratic formula
D: Do the results in A, B, differ from each other? Why or Why not?
You must mean
k^2 + 4k = 0
factoring:
k(k+4) = 0
so k=0 or k= -4
formula:
x = (-4 ± √(16 - 4(1)(0))/2
= (-4 ± 4)/2
= 0 or -4
why should they differ??? Both are valid methods.
To solve the equation k^2 + 4k = 0, we can use two methods: factoring and quadratic formula.
A: Factoring method:
To factor this equation, we need to find two values that multiply to zero. In this case, k^2 + 4k = 0, so we set each term equal to zero and solve for k.
k^2 = 0 or 4k = 0
From the first equation, we can see that k must be equal to zero.
From the second equation, we divide both sides by 4 to find k.
k = 0 or k = -4/4 Simplifying, we get k = -1.
Therefore, the solution to the equation k^2 + 4k = 0 using the factoring method is k = 0, -1.
B: Quadratic formula method:
The quadratic formula is used to solve any quadratic equation of the form ax^2 + bx + c = 0, where a, b, and c are constants.
In this case, a = 1, b = 4, and c = 0.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac))/2a
Plugging in the values from our equation, we get:
k = (-4 ± √(4^2 - 4(1)(0)))/2(1)
k = (-4 ± √(16))/2
k = (-4 ± 4)/2
Simplifying further, we get:
k = -1 or k = 0
Therefore, the solution to the equation k^2 + 4k = 0 using the quadratic formula is k = -1, 0.
D: The results obtained from both methods, A and B, are the same. Both methods are accurate and valid ways to solve quadratic equations. The factoring method and quadratic formula are based on different principles, but they yield the same solutions when applied correctly. In this case, the solutions k = 0 and k = -1 are common to both methods.