Rewrite the given quadratic equation in standard form: Kx 2 + 2x - 1 = 0
Discriminant = 4 - 4(K)(-1) = 4 + 4K
For the equation to have two real solutions, the discriminant has to be positive. Hence we need to solve the inequality 4 + 4K > 0.
The solution set to the above inequality is given by: K > -1 for which the given equation has two real solutions.
Answer:
<em>f(x) = x² (2+i)x-15-3i</em>
Step-by-step explanation:
Since the zeros of the equation are -3 and 5+i, hence the factors of the polynomial in x is (x+3) and (x-(5+i))
Multiplying both factors
f(x) = (x+3)(x-(5+i))
f(x) = (x²-(5+i)x+3x -3(5+i))
f(x) = x² - (5+i- 3)x -15-3i
f(x) = x² (2+i)x-15-3i
<em>hence the required polynomial function in x is f(x) = x² (2+i)x-15-3i</em>
Answer:
Th Range is [0, -∞)
Step-by-step explanation:
f(x) = 2 - x
w(x) = x - 2
We want to find the range of (f * w)(x).
First, we need to find (f * w)(x), which is the multiplication of the function f(x) and the function w(x). Lets use algebra to find (f * w)(x):
This is a quadratic function (U shaped), or a parabola. The graph is attached.
The range is the set of y-values for which the function is defined.
We see from the graph that the parabola is upside down and the highest value is y = 0 and lowest goes towards negative infinity. So the range is from 0 to negative infinity. Or,
0 < y < ∞
In interval notation, that would be:
[0, -∞)
You have to show the question more I can’t see the graph
x-2y = -2
x-2(-3x+8)=-2
mutiply the bracket by -2
(-2)(-3x)=6x
(-2)(8)=-16
x+6x-16=-2
7x-16=-2
move -16 to the other side
sign changes from -16 to +16
7x-16+16=-2+16
7x= -2+16
7x= 14
divide both sides by 7
7x/7=14/7
x=2
Find y by using the substitution method
y=-3x+8
y=-3(2)+8
-6+8
=2
Answer:(2,2)
