Question

First options are Keith JordanRandellSecond Options are 3 and 45 and 12 -60 and -770 and -17-5 and -1220 and 21

Answer 1

We are given a quadratic equation and asked to decipher who got it right.

Our approach is to use the factorization method of resolving quadratic equations to come up with the solution. We can afterward figure out the wrong and right technique.

Given:

`x^2+17x+72=12`

The equation is not in the standard form of quadratic equations that ought to help us solve quadratic equations.

We will put it in the standard form.

`\begin{gathered} x^2+17x+72=12 \\ \text{ Subtract 12 from both sides} \\ x^2+17x+60=0 \end{gathered}`

Now we have it in standard form, solving via factorization will require us to find 2 factors of the 3rd term that add up to the 2nd term.

`\begin{gathered} x^2+17x+60=0 \\ 12\text{ and 5 are 2 factors of }60\text{ that add up to 17} \\ x^2+12x+5x+60=0 \\ x(x+12)+5(x+12)=0 \\ (x+12)(x+5)=0 \\ (x+5)=0\text{ or }(x+12)=0 \\ x=-5\text{ OR }x=-12 \end{gathered}`

Keith solved the equation to be x = -5 or x = -12