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3 years ago

Select all the zeros of the following polynomial F(x)=(x-3)(x+2)(x-4)

1 answer:

5 0

Answer: (B) -2, (E) 1, (F) 2
Step-by-step explanation:
x³ - x² - 4x + 4
= x²(x - 1) - 4(x - 1)
= (x² - 4) (x - 1)
= (x - 2)(x + 2)(x - 1)
Set each factor equal to zero to find the roots:
x - 2 = 0 x + 2 = 0 x - 1 = 0
x = 2 x = -2 x = 1

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2. Find the general relation of the equation cos3A+cos5A=0

mars1129 [50]

<h2>Answer:</h2>

$A=\frac{\pi}{8}+\frac{n\pi}{4}or\ A=\frac{\pi}{2}+n\pi$

<h2>Step-by-step explanation:</h2>

<h3>Find angles</h3>

$cos3A+cos5A=0$

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<h3>Transform the expression using the sum-to-product formula</h3>

$2cos(\frac{3A+5A}{2})cos(\frac{3A-5A}{2})=0$

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<h3>Combine like terms</h3>

$2cos(\frac{8A}{2})cos(\frac{3A-5A}{2})=0\\\\ 2cos(\frac{8A}{2})cos(\frac{-2A}{2})=0$

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<h3>Divide both sides of the equation by the coefficient of variable</h3>

$cos(\frac{8A}{2})cos(\frac{-2A}{2})=0$

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<h3>Apply zero product property that at least one factor is zero</h3>

$cos(\frac{8A}{2})=0\ or\ cos(\frac{-2A}{2})=0$

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<h3>Cross out the common factor</h3>

$cos\ 4A=0$

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<h3>Solve the trigonometric equation to find a particular solution</h3>

$4A=\frac{\pi}{2}or\ 4A=\frac{3\pi}{2}$

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<h3>Solve the trigonometric equation to find a general solution</h3>

$4A=\frac{\pi}{2}+2n\pi \ or\\ \\ 4A=\frac{3 \pi}{2}+2n \pi\\ \\A=\frac{\pi}{8}+\frac{n \pi}{4\\}$

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<h3>Reduce the fraction</h3>

$cos(-A)=0$

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<h3>Simplify the expression using the symmetry of trigonometric function</h3>

$cosA=0$

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<h3>Solve the trigonometric equation to find a particular solution</h3>

$A=\frac{\pi }{2}\ or\ A=\frac{3 \pi}{2}$

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<h3>Solve the trigonometric equation to find a general solution</h3>

$A=\frac{\pi}{2}+2n\pi\ or\ A=\frac{3\pi}{2}+2n\pi,n\in\ Z$

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<h3>Find the union of solution sets</h3>

$A=\frac{\pi}{2}+n\pi$

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<h3>Find the union of solution sets</h3>

$A=\frac{\pi}{8}+\frac{n\pi}{4}\ or\ A=\frac{\pi}{2}+n\pi ,n\in Z$

<em>I hope this helps you</em>

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