three of the roots of the equation ax^5 + bx^4 + cx^3 + dx^2 + ex + f are -2, 2i and 1 + 1i. Find the values of a, b, c, d, e and f.
I hope he finds this.
And if you do find it, **** you.
Easy 10.
I hope he finds this.
And if you do find it, **** you.
Easy 10.
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Since 2i and 1+i are zeros, so are their conjugates −2i and 1−i
When x = r is a root of f(x), then (x−r) is a factor of f(x)
f(x) = a (x+2) (x−2i) (x+2i) (x−1−i) (x−1+i)
f(x) = a (x+2) (x²+4) (x²−2x+2)
f(x) = a (x⁵ + 2x³ + 4x² − 8x + 16)
Now we can see that there are infinite values for a, c, d, e, f (b is always = 0)
When a = 1 ----> b = 0, c = 2, d = 4, e = −8, f = 16
When a = 2 ----> b = 0, c = 4, d = 8, e = −16, f = 32
When a = −1 ----> b = 0, c = −2, d = −4, e = 8, f = −16
etc.....
When x = r is a root of f(x), then (x−r) is a factor of f(x)
f(x) = a (x+2) (x−2i) (x+2i) (x−1−i) (x−1+i)
f(x) = a (x+2) (x²+4) (x²−2x+2)
f(x) = a (x⁵ + 2x³ + 4x² − 8x + 16)
Now we can see that there are infinite values for a, c, d, e, f (b is always = 0)
When a = 1 ----> b = 0, c = 2, d = 4, e = −8, f = 16
When a = 2 ----> b = 0, c = 4, d = 8, e = −16, f = 32
When a = −1 ----> b = 0, c = −2, d = −4, e = 8, f = −16
etc.....