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Marizza181 [45]
3 years ago
15

What are the zeros of the function? h(x)=x^3−2x^2−3x

Mathematics
1 answer:
maksim [4K]3 years ago
3 0
To find the zeroes you make the function equal to zero and then solve. 
0=x^3-2x^2-3x
Then factor out the x to get a quadratic inside the parentheses.
 0=x(x^2-2x-3)
Factor the inside quadratic formula.
x(x^2-2x-3)=x((x-3)(x+1))
Lastly, use the zero product property to solve.
x*(x-3)*(x+1)=0
x=0,x=3,x=-1
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Answer:

\rm x = \dfrac{2+\sqrt{10}}{3},\dfrac{2-\sqrt{10}}{3}

Step-by-step explanation:

A quadratic equation is given to us and we need to solve the equation using the quadratic formula . The given equation is ,

\rm\implies 3x^2=2(2x+1)

Open the brackets in RHS ,

\rm\implies 3x^2= 4x + 2

Transpose all the terms to LHS ,

\rm\implies 3x^2-4x-2=0

The general form of a quadratic equation is ax² + bx + c = 0 , and the roots of the equation by the Quadratic Formula ( Shreedhacharya's Formula ) is given by ,

\rm\implies\red{ x =\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}

Using the quadratic formula , we have ,

\rm\implies x =\dfrac{-(-4) \pm \sqrt{(-4)^2-4(3)(-2) }}{2(3)}

Simplify ,

\rm\implies x =\dfrac{4 \pm \sqrt{16+24 }}{6}

\rm\implies x = \dfrac{4\pm \sqrt{40}}{6}

\rm\implies x =\dfrac{4\pm 2\sqrt{10}}{6}

\rm\implies\boxed{\pink{\frak{ x = \dfrac{2+\sqrt{10}}{3},\dfrac{2-\sqrt{10}}{3}}}}

8 0
2 years ago
Determine the unit rate of a marathon runner who travels 9/2 miles in 3/4 hour.
ludmilkaskok [199]

Answer:

The marathon runner runs 1 mile every 10 minutes.

Step-by-step explanation:

9/2 miles is equal to 4.5 miles. 3/4 hours is equal to 45 minutes.

8 0
3 years ago
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3 years ago
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Step-by-step explanation:

Use the trick of shaking everybodys hand

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8 0
3 years ago
What is the solution to the equation 5x = 40?
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40 divided by 5 is 8.
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OR we can do it another way.
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Now we have 8. Still.
X is 8
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2 years ago
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