Write the quadratic equation whose roots are −6 and −5, and whose leading coefficient is 1.(Use the letter x to represent the variable.)
Question
Write the quadratic equation whose roots are −6 and −5, and whose leading coefficient is 1.(Use the letter x to represent the variable.)
Solution
The quadratic equation can be found using the formula:
x^2 - (sum of the roots)x + (product of the roots) = 0
Given that the roots are -6 and -5, we can substitute these values into the formula:
x^2 - ((-6) + (-5))x + ((-6) * (-5)) = 0
This simplifies to:
x^2 - (-11)x + 30 = 0
Multiplying through by -1 to make the leading coefficient positive gives:
x^2 + 11x - 30 = 0
So, the quadratic equation whose roots are -6 and -5, and whose leading coefficient is 1 is x^2 + 11x - 30 = 0.
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