Chapter 4, Problem 5AR

To determine

To Solve: The quadratic equation $y^2=13y$ using factoring or quadratic formula.

Answer to Problem 5AR

The solution of equation is either $y=13$ or $y=0$

Explanation of Solution

Given information:

The quadratic equation $y^2=13y$

Concept and Formula Used:

Quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ where quadratic equation is $a{x}^2+bx+c=0$

Solving using factoring can be done by splitting the middle term of equation and then making groups and equating them to zero.

Calculation:

It is given that

  $y^2=13y$

The equation can be written as $y^2-13y=0$

Solving equation using quadratic formula $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Where $a=1,b=-13\&c=0$

Putting the values in the formula

  $\begin{array}{l}y=\frac{-\left(-13\right)\pm \sqrt{{\left(-13\right)}^2-4\times \left(1\right)\times \left(0\right)}}{2\left(1\right)}\\ y=\frac{13\pm \sqrt{169-0}}{2}\\ y=\frac{13\pm \sqrt{169}}{2}\\ y=\frac{13\pm 13}{2}\end{array}$

Therefore either $y=\frac{13+13}{2}=\frac{26}{2}$ or $y=\frac{13-13}{2}=0$

Either $y=13$ or $y=0$

Conclusion:

The solution of equation is either $y=13$ or $y=0$