# Thread: Few Questiosn regarding Graphs and equations

1. ## Few Questiosn regarding Graphs and equations

1.Find a cubic equation with integral coefficients with roots 3i and -5

2.Does this work with quadratic equations as well?

3.Find all real and imaginary roots of X^3-3x^2+4x-12=0(do i use synthetic division to find all the roots?)

2. Originally Posted by xian791
1.Find a cubic equation with integral coefficients with roots 3i and -5

2.Does this work with quadratic equations as well?

3.Find all real and imaginary roots of X^3-3x^2+4x-12=0(do i use synthetic division to find all the roots?)
1. $y = k(x + 3i)(x - 3i)(x + 5)$

2. yes

3. $x^3-3x^2+4x-12=0$

$x^2(x - 3) + 4(x - 3) = 0$

$(x-3)(x^2+4) = 0$

finish up

3. for the first one, how did you get the answer? What does k stand for and you add and subtract 3i, but why not add and subtract 5?

4. k is just a constant which depends on what points (x,y) the cubic function passes through.

if a polynomial has a root $a + bi$, then its conjugate $a - bi$ is also a root.

5 is a single root.

5. im still a bit confused on the answer...

lets say they gave u 8 and 3 and they wanted you to find the quadratic equation.How would you solve it?

6. if $x = 8$ and $x = 3$ are zeros of the quadratic function, then $y = k(x-3)(x-8)$