Write a quadratic equation in the form x^2+bx+c=0x 2 +bx+c=0 that has the following roots: Roots: 6±7i

Answer 1

f(x) = x^2 -12x + 85

reverse engineer this, like Prof. Sheldon Cooper figuring out Howard's card trick

x=6+or - 7i

x-6 = + or - 7i

square both sides

(x-6)^2 = -49

x^2 -12x + 36 = -49

x^2 -12 + 85

It has vertex or minimum point (6,49) and it's an upward opening parabola with y intercept 85

It never crosses the x axis, so it's solutions or zeroes are imaginary

Answer 2

Use the factored form of the quadratic:

0 = a·(x-p)·(x-q)

where a is a constant and p and q are the roots, 6+7i and 6-7i.

0 = a·(x - (6+71))·(x-(6-7i) = a·(x-6-71)·(x-6+7i)

Since we can write any quadratic with these roots, we can choose the value of a. It is simplest to choose a = 1, so our equation is:

y = (x-6-71)·(x-6+7i)

To put it into the standard form that the problem asks for, multiply the factors together then arrange it in descending powers of x.

Answer 3

Watch this: https://www.youtube.com/watch?v=ZJcpQDL1J8M