Question

Write a quadratic equation with the given roots. Write the equation in the form , where a, b, and c are integers. –7 and –2

Answer 1

`\bf x= \begin{cases} -7\\ -2 \end{cases}\implies \begin{cases} x=-7\implies &x+7=0\\ x=-2\implies &x+2=0 \end{cases}\implies (x+7)(x+2)=\stackrel{y}{0} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\mathbb{FOIL}}{x^2+9x+14=y}~\hfill`

Answer 2

For this case we have that a quadratic equation is of the form:

`ax ^ 2 + bx + c = 0`

If you tell us that the solutions are given by:

`x_(1)=-7\\x_ {2}=-2`

So, we have:

`(x + 7)(x + 2) = 0`

We apply distributive property:

`x ^ 2 + 2x + 7x + 14 = 0`

We add similar terms:

`x ^ 2 + 9x + 14 =0`

Answer:

`x^2+9x+14=0`

`a=1\\b=9\\c=14`