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:
- Substitute the values of \( r_1 \) and \( r_2 \):
\[ (x - 6)(x - 8) = 0 \]
- 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:
\[ x^2 - 14x + 48 = 0 \]
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