Form a quadratic equation ax2+bx+c=0 with a=1 that has the given roots:
−1±i 2
same kind of problem I just did for you,
follow the same steps
To form a quadratic equation with the given roots, we can use the fact that the roots of a quadratic equation in the form of ax^2 + bx + c = 0 can be found using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Given that one of the roots is -1 + i2, we know that its conjugate is also a root, which is -1 - i2. So we have two roots: -1 + i2 and -1 - i2.
To find the equation, we can set up two binomial factors:
(x - (-1 + i2))(x - (-1 - i2)) = 0
Multiplying these out gives:
(x + 1 - i2)(x + 1 + i2) = 0
Using the difference of squares formula (a^2 - b^2 = (a + b)(a - b)), we can simplify further:
[(x + 1)^2 - (i2)^2] = 0
Simplifying the expression within the brackets:
(x + 1)^2 - (i^2)(2^2) = 0
(x + 1)^2 - (i^2)(4) = 0
(x + 1)^2 - (-1)(4) = 0
(x + 1)^2 + 4 = 0
This is the quadratic equation with the roots -1 + i2 and -1 - i2 when a = 1:
x^2 + 2x + 5 = 0