Algebra
Quadratic Equations
Consider the quadratic equation \(7 x^2 = 49 x\). What is the sum of all the roots of this equation?
If the following statement is true, what is the value of \(a\): \[x^2+5x-14=(x+a)(x-2)?\]
What are the roots of the quadratic equation \[2(x+2)^2-33=13x+8 ?\]
What are the roots of the quadratic equation \[ix^2+(7-4i)x-12-12i=0 ?\]
Details and assumptions
\(i\) is the imaginary number that satisfies \(i^2 = -1\).
If \[x^2-8x+15=(x+a)(x+b),\] what is the value of \(ab\)?