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.
Similar Questions
Write the quadratic equation whose roots are −1 and 4, and whose leading coefficient is 4.(Use the letter x to represent the variable.)
What are the roots of the quadratic equation x^2 - 5x + 6 = 0 ?a.x = -2, x = -3b.x = -2, x = 3c.x = 2, x = -3d.x = 2, x = 3
Use the quadratic formula to solve. Express your answer in simplest form.6, x, squared, minus, 5, x, minus, 2, equals, minus, 6, x, squared6x 2 −5x−2=−6x 2
Use the calculation below to write out the original quadratic equation.x=−5±52−4(−3)(1)−−−−−−−−−−−√2(−3)
The zeros of a quadratic function are 6 and -4. Which of these choices could be the function?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.