Question

Supply the number so that the quadratic equation below has 6 and 8 as its solutions.

Answer 1

To form a quadratic equation based on its roots (solutions), you can use the fact that if \( r_1 \) and \( r_2 \) are the roots of the equation, the quadratic can be expressed in the form:

\[
(x - r_1)(x - r_2) = 0
\]

Given roots \( r_1 = 6 \) and \( r_2 = 8 \), the equation can be constructed as follows:

1. Substitute the values of \( r_1 \) and \( r_2 \):

\[
(x - 6)(x - 8) = 0
\]

2. Expand the expression:

\[
x^2 - 8x - 6x + 48 = 0
\]
\[
x^2 - 14x + 48 = 0
\]

Thus, the quadratic equation is:

\[
x^2 - 14x + 48 = 0
\]

In conclusion, the quadratic equation that has 6 and 8 as solutions is:

\[
x^2 - 14x + 48 = 0
\]