When roots of polynomials occur in radical form, they occur as two conjugates.
That is,
The conjugate of (a + √b) is (a - √b) and vice versa.
To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.
The first factor is x - (a + √b).
The second factor is x - (a - √b).
The polynomial is
f(x) = [x - (a + √b)]*[x - (a - √b)]
= x² - x(a - √b) - x(a + √b) + (a + √b)(a - √b)
= x² - 2ax + x√b - x√b + a² - b
= x² - 2ax + a² - b
This is a quadratic polynomial, as expected.
If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.
x = (1/2) [ 2a +/- √(4a² - 4(a² - b)]
= a +/- (1/2)*√(4b)
= a +/- √b
x = a + √b, or x = a - √b, as expected.
Answer:
y = 4x + 4
Step-by-step explanation:
Two points you can see on the graph are (0,4) and (-2,-4)
Now, to find the slope, use delta y/ delta x
(-4-4)/(-2-0)
(-8)/(-2) = 4
Slope is 4.
y = 4x + b
Now, to find b, we need the y-intercept, which is the point where x is 0 and the graph crosses the y-axis.
This value is 4. So, the y-intercept is 4
Substitute into your equation
y = 4x + 4
Answer: 50 meters
Step-by-step explanation: I just finished the pretest
Answer:
look do is gone eat
Step-by-step explanation:
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