Question

10.Work backwards to write a quadratic equation that will have solutions of x = 3 and x = -7. 11.Work backwards to write a quadratic equation that will have solutions of x = 12 and x = 2. 12.Work backwards to write a quadratic equation that will have solutions of x = -1/2 and x = 4. (Your equation must only have integer coefficients, meaning no fractions or decimals.) 13. Write a quadratic equation that will have a solution of only x = 0. Note: this means there will be a double solution of x = 0. 14. Write a quadratic equation that cannot be factored.

Answer 1

Explanation

Question 10

We are asked to write the quadratic eqation that has the solutions of x=3 and x =-7

To do so, we will make use of

$y=x^2-(sum\text{ of roots})x+product\text{ of roots}$

So we will follow the steps below

$\begin{gathered} Sum\text{ of roots = 3+}-7=-4 \\ product\text{ of roots =3\lparen-7\rparen=-21} \end{gathered}$

substituting the above, we will have

$\begin{gathered} x^2-(-4)x+(-21)=0 \\ \\ x^2+4x-21=0 \end{gathered}$

Therefore, the quadratic equation is

$x^2+4x-21$