1)y=x²-3x+2
2)y=8x-16/x-3
A)Sketch both on axes
B)Calculate coordinate of points of intersection
I have drawn both on axes. I am having trouble with B). I know you have to do y=y.
So far i have done this;
x²-3x+2=8x-16/x-3
(x-3)(x²-3x+2)=8x-16
x³-6x²+11x-6=8x-16
x³-6x²+3x=-16
x³-6x²+3x+16=0
what do i do now?
little mistake:
when you multiply 8x-16/x-3 by x-3
u have to multiply 8x too
To find the coordinates of the points of intersection between the two equations, you need to solve the equation x³ - 6x² + 3x + 16 = 0.
Here are the steps to follow:
1. Start by using the Rational Root Theorem to determine possible rational roots of the equation. The rational root theorem states that if a polynomial equation has a rational root p/q, where p and q are integers with no common factors other than 1, then p must be a factor of the constant term (in this case, 16), and q must be a factor of the leading coefficient (in this case, 1). Possible rational roots of this equation are ±1, ±2, ±4, ±8, ±16.
2. Use synthetic division or another method to test each of the possible rational roots from step 1. Plug the values into the equation and see if they make the equation equal to zero.
3. After finding a root, divide the original equation by the corresponding binomial factor (x - root) using polynomial long division or synthetic division.
4. Repeat steps 1-3 with the resulting quotient until you find all the roots of the equation.
Once you have the values of x where the two equations intersect, substitute these values into either equation to find the corresponding y-values.
If you need assistance with the calculation, let me know the values you have tried, and I can help you further.