12.7k views
5 votes
A certain quadratic polynomial has solutions x=4 and x=0. Create an equation that could represent this quadratic polynomial.

User Cement
by
7.6k points

1 Answer

5 votes

Answer:

(x-4)x = 0

Explanation:

If we have a quadratic equation of the form


(x-a)(x-b)=0

it has solutions at x = a and x = b because putting either one of these values into the above equation satisfies it. For example, putting in x = a gives


\begin{gathered} (a-a)(x-b)=0 \\ 0(x-b)=0 \\ 0=0 \end{gathered}

this satisfies the equation and likewise for x = b.

Hence, if we want to construct an equation which has solutions x = 4 and x = 0, we just need to set a = 4 and b = 0. Doing this gives


\begin{gathered} (x-4)(x-0)=0 \\ (x-4)x=0 \end{gathered}

which is a polynomial that has the solutions desired.

User Kiesha
by
8.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories