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Answer:
BiG ChUnGuS moo
Step-by-step explanation:
x^2 = 16/100
We must solve for x by taking the square root of both sides.
But imagine x^2 = 9. x = 3 is a solution because 3^2 = 9. But x = -3 is also a solution because (-3)^2 = 9. So we need to add the plus and minus sign to account for all of our solutions.
√x^2 = √(16/100)
We square root both sides to remove the exponent 2 on x. Then
x = ±√(16/100)
Then we have to use a Property of Radicals which is √(x/y) = √(x) / √(y).
Then the square root of 16 is 4 and the square root of 100 is 10. 4/10 is 2/5 simplified.
Answer:
y = x³ + 10.5x² + 31x + 13
Step-by-step explanation:
Complex roots (roots that have imaginary terms) always come in conjugate pairs. So if one root is -5 + i, there's another root that's -5 − i.
So the polynomial is:
y = (x + 1/2) (x − (-5 + i)) (x − (-5 − i))
Distributing:
y = (x + 1/2) (x² − (-5 + i)x − (-5 − i)x + (-5 + i)(-5 − i))
y = (x + 1/2) (x² + 5x − ix + 5x + ix + (-5 + i)(-5 − i))
y = (x + 1/2) (x² + 10x + (-5 + i)(-5 − i))
y = (x + 1/2) (x² + 10x + 25 + 5i − 5i − i²)
y = (x + 1/2) (x² + 10x + 25 + 1)
y = (x + 1/2) (x² + 10x + 26)
y = x(x² + 10x + 26) + 1/2(x² + 10x + 26)
y = x³ + 10x² + 26x + 1/2x² + 5x + 13
y = x³ + 10.5x² + 31x + 13
