Write the quadratic function whose zeros are:
1. 2+square root of 5, 2-square root of 5
2. 3+7i,3-7i
3. 5±i
Please tell me how to get them. I have no clue on how to solve them.
For any quadratic equation, if you have irrational or complex roots, they will always come as conjugate pairs, just like your given roots
method one:
use the fact that if x=a is a root, then x-a will be a factor of your equation, so
1.
(x - (2+√5))(x - (2-√5) = 0
(x-2 - √5)(x - 2 + √5) = 0
x^2 - 2x + √5x - 2x + 4 - 2√5 - √5x + 2√5 - 5 = 0
x^2 - 4x - 1 = 0
method 2:
use the property that for x^2 + bx + c = 0
the sum of the roots is -b and the product of the roots is c
1. sum of roots = 2+√5 + 2-√5 = 4
product of the roots = (2+√5)(2-√5) = 4 - 5 -1
so the equation is
x^2 -4x - 1 = 0
use either method for your other two equations.
check by finding their roots.