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Quadratic Equations

Quadratic equations describe the motion of a baseball after it connects with a bat, and the acceleration of gravity at the Earth's orbit.

Factoring

         

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 \(ab\)?

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