SOLUTION: how many zeros are in the solution to the function g(x)=x^2-3x+4.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: how many zeros are in the solution to the function g(x)=x^2-3x+4.      Log On


   



Question 1090564: how many zeros are in the solution to the function g(x)=x^2-3x+4.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
g%28x%29=x%5E2-3x%2B4...this is quadratic function, and it may have one, two, or zero roots
The discriminant b%5E2-4%2Aa%2Ac is important because it tells you how many roots a quadratic function has.
1. b%5E2-4%2Aa%2Ac%3C0 There are no+real roots.(there will two complex roots)
2. b%5E2-4%2Aa%2Ac=0 There is one+real root.
3. b%5E2-4%2Aa%2Ac%3E0 There are two+real roots.

in your case b%5E2-4%2Aa%2Ac=%28-3%29%5E2-4%2A1%2A4=-7 => b%5E2-4%2Aa%2Ac%3C0 and there is no+real roots (there will two complex roots)
check using quadratic formula:
g%28x%29=x%5E2-3x%2B4
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-3%29%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A4+%29%29%2F%282%2A1%29+
x+=+%283%2B-+sqrt%28+9-16+%29%29%2F2+
x+=+%283%2B-+sqrt%28+-7+%29%29%2F2+
x+=+%283%2B-+i%2Asqrt%28+7+%29%29%2F2+
complex solutions:
x+=+3%2F2%2B+i%2Asqrt%28+7+%29%2F2+
x+=+3%2F2-+i%2Asqrt%28+7+%29%2F2+