SOLUTION: If 4 + I and 4 - I are roots of the equation z^2 + az + b = 0 find the value of a and the value of b? For the format: ax² + bx + c = 0 Sum of the roots = - b/a Product

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Question 1017157: If 4 + I and 4 - I are roots of the equation z^2 + az + b = 0 find the value of a and the value of b?
For the format: ax² + bx + c = 0
Sum of the roots = - b/a
Product of the roots = c/a
given: (4 + i) and (4 - i)
8 = - b/a
17 = c/a
a = (- b)/8 = 1
- b = 8
b = - 8
a = c/17 = 1
c = 17
equation is: z² - 8z + 17 = 0
check...do something
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
If 4 + I and 4 - I are roots of the equation z^2 + az + b = 0 find the value of a and the value of b?
-------------------------------------------- 

Since the quadratic equation has the coefficient "1" as the leading coefficient (at ), then 

z1 + z2 = -a,
Z1*z2 = b.

Hence, a = (4+i)*(4-i) = 16 -  = 16 - (-1) = 16 + 1 = 17.

       b = (4+i) + (4-i) = 8.

That is all.


Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
If 4 + I and 4 - I are roots of the equation z^2 + az + b = 0 find the value of a and the value of b?
For the format: ax² + bx + c = 0
Sum of the roots = - b/a
Product of the roots = c/a
given: (4 + i) and (4 - i)
8 = - b/a
17 = c/a
a = (- b)/8 = 1
- b = 8
b = - 8
a = c/17 = 1
c = 17
equation is: z² - 8z + 17 = 0
check...do something
Who writes these RIDICULOUS math problems?

The general form of a quadratic equation is: , or in this case: . Why give: ?

Why would a quadratic equation be written with the NORMAL variable on : "a" as the variable on "x", and the NORMAL

variable on x: "b," as the constant: "c."? Why do these people make these RIDICULOUSLY confusing math problems?

Anyway, you're correct, the variable on z, or , and the constant, or variable, , for the quadratic equation:  

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