Use the graph of the polynomial function to find the factored form of the related polynomial. Assume it has no constant factor.
2 answers:
Answer with explanation:
I will use cubic polynomial to explain this.Let the graph of the polynomial cuts the X axis at , a, b and c.Suppose all the three roots of the cube are Real.
So, it has three roots equal to a, b and c.
Equation of Cubic Polynomial is given by:
= (x-a)(x-b)(x-c)
= [x² - (a+b)x + a b](x-c)
= x²(x -c)-x(a+b)(x-c)+ab(x-c)
= x³-x²c- (x²-xc)(a+b)+a b x - a b c
= x³ - x² c-x² a - x² b+a c x + b c x+a b x - a b c
=x³-x²(a+b+c)+x(a b+b c+ca)-a b c
The factors a, b and c can be any rational number in the form of
For example ,the roots of the cubic polynomial are 1, -1 and 3.
Polynomial Function = (x -1)[x-(-1)](x-3)
=(x-1)(x+1)(x-3)
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Answer:
Step-by-step explanation:
We can use either angle, but I'm going to use the one on the bottom. So, in order to find x, we need to use tangent. One side we know is the adjacent, and the side we don't know is the opposite, therefore we need tangent. Here's the equation:
Obviously, we can't have a root in our denominator, so we need to get rid of it somehow. Here's how:
We multiply the denominator of the fraction by .
multiplied by itself is simply 2. Try it! We also want to multiply the numerator by
, but there isn't really a number we can use with that, so we'll just add it to the side. The equation you have now is:
Let's try to work this out now. Since the denominator is 2, we have to multiply both sides by it to find x.
We can plug 2 in for the x in the numerator now:
2 and 2 cancel out, so you get 1 in both the numerator and denominator. That's how we get our answer of
Also, because this is a 45-45-90 triangle, you don't really have to do all that work. If it's a 45-45-90 triangle, both legs should be the same length. :)