Find and label -0 on the number line. Explain. Does -0 just mean 0?
1 answer:
The opposite of the number 0 that is -0 on the number line will be equal to 0 itself.
A number line may be defined as a scale consisting of numbers labelled from 0 to 9 which are used to plot or mark different points for various entities. Number line extends from 0 to 9 in the positive side that is usually taken as right-hand side and it extends from 0 to -9 in the negative side that is usually taken as the left-hand side. The numbers on the right-hand side of number line have their opposites on the left-hand side. The opposite of a number x is taken as -x. For example, the opposite of 4 is taken as -4 and 4 lies on right-hand side whereas -4 lies on left-hand side. 0 lies on the center of number line and is taken as the main point. It is neither positive nor negative so the opposite of 0 is 0. The figure of number line is attached.
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Starting off with the polynomial in standard form would be extremely difficult, but we can construct one fairly easily with the zeroes we've been given.
We know from the given zeroes that our function has the value 0 when x = 1, x = -2, and x = 2. Manipulating each equation, we can rewrite them as x - 1 = 0, x + 2 = 0, and x - 2 = 0. To construct our polynomial, we simply use all three of the expressions on the left side of the equation as factors and multiply them together, obtaining:
Notice that we can easily obtain each our three zeroes by dividing both sides by the two other factors. From here, we just need to expand the left-hand side of the equation. I'll show the work required here:
=0\\ (x^2-x+2x-2)(x-2)=0\\ (x^2+x-2)(x-2)=0\\ (x^2+x-2)x-(x^2+x-2)2=0\\ x^3+x^2-2x-(2x^2+2x-4)=0\\ x^3+x^2-2x-2x^2-2x+4=0\\ x^3+(x^2-2x^2)+(-2x-2x)+4=0\\ x^3-x^2-4x+4=0\\](https://tex.z-dn.net/?f=%28x-1%29%28x%2B2%29%28x-2%29%3D0%5C%5C%0A%5Cbig%5B%28x-1%29x%2B%28x-1%292%5Cbig%5D%28x-2%29%3D0%5C%5C%0A%28x%5E2-x%2B2x-2%29%28x-2%29%3D0%5C%5C%0A%28x%5E2%2Bx-2%29%28x-2%29%3D0%5C%5C%0A%28x%5E2%2Bx-2%29x-%28x%5E2%2Bx-2%292%3D0%5C%5C%0Ax%5E3%2Bx%5E2-2x-%282x%5E2%2B2x-4%29%3D0%5C%5C%0Ax%5E3%2Bx%5E2-2x-2x%5E2-2x%2B4%3D0%5C%5C%0Ax%5E3%2B%28x%5E2-2x%5E2%29%2B%28-2x-2x%29%2B4%3D0%5C%5C%0Ax%5E3-x%5E2-4x%2B4%3D0%5C%5C)
So, in standard form, our cubic polynomial would be
We know from the given zeroes that our function has the value 0 when x = 1, x = -2, and x = 2. Manipulating each equation, we can rewrite them as x - 1 = 0, x + 2 = 0, and x - 2 = 0. To construct our polynomial, we simply use all three of the expressions on the left side of the equation as factors and multiply them together, obtaining:
Notice that we can easily obtain each our three zeroes by dividing both sides by the two other factors. From here, we just need to expand the left-hand side of the equation. I'll show the work required here:
So, in standard form, our cubic polynomial would be