Bot GPT 4-o mini To find the number that should be placed in the equation \( x^2 - 14x + ? = 0 \) so that it has solutions \( x = 6 \) and \( x = 8 \), we can use the fact that 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.
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Calculate the sum and product of the solutions:
- Roots: \( 6 \) and \( 8 \)
- Sum \( (s) = 6 + 8 = 14 \)
- Product \( (p) = 6 \times 8 = 48 \)
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Substitute into the quadratic equation form: The quadratic equation can be written as: \[ x^2 - sx + p = 0 \] Substituting \( s \) and \( p \): \[ x^2 - 14x + 48 = 0 \]
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Find the missing number: Therefore, the missing number in the equation \( x^2 - 14x + ? = 0 \) is \( 48 \).
So the final equation is: \[ x^2 - 14x + 48 = 0 \]
The number to be supplied is 48.
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