Q: Write a quadratic equation with integral coefficients whose roots are -6+i and -6-i
My Answer: x^2+12x+37
(first) sum=-12
product=37
(then) write equation using formula x^2-(sum)x+product
Is my work and answer correct?
You are correct.
Yes, your work and answer are correct. Well done!
Yes, your work and answer are correct! Well done.
To find a quadratic equation with roots -6+i and -6-i, you can use the fact that complex roots always come in conjugate pairs. This means that if -6+i is a root, then -6-i must also be a root.
Using the sum and product of the roots, you correctly determined that the sum of the roots is -12 and the product of the roots is 37. With these values, you can form the quadratic equation using the formula:
x^2 - (sum)x + product = 0
Substituting the values obtained:
x^2 - (-12)x + 37 = 0
x^2 + 12x + 37 = 0
So, your final answer of x^2 + 12x + 37 is indeed the correct quadratic equation with integral coefficients whose roots are -6+i and -6-i.