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

Question

x^2-14x+___ =0

Answer 1

To find the missing number in the quadratic equation \( x^2 - 14x + __ = 0 \) which has solutions \( 6 \) and \( 8 \), we can use Vieta's formulas. According to Vieta's formulas, for a quadratic equation of the form \( x^2 - (s)x + p = 0 \), where \( s \) is the sum of the roots and \( p \) is the product of the roots, we have:

1. Sum of the roots (\( s \)): \[ s = 6 + 8 = 14 \]

2. Product of the roots (\( p \)): \[ p = 6 \times 8 = 48 \]

Now, we can rewrite the quadratic equation using the values of \( s \) and \( p \): \[ x^2 - 14x + 48 = 0 \]

Thus, the number that should replace the blank is 48.