SOLUTION: 1. Use the discriminant to determine the number of solutions for x^2-3x+6=0 2. Solve x^2+6x=0 3. Solve the following quadratic equation using the specified method. (5 points

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 1. Use the discriminant to determine the number of solutions for x^2-3x+6=0 2. Solve x^2+6x=0 3. Solve the following quadratic equation using the specified method. (5 points       Log On


   

Question 1085809: 1. Use the discriminant to determine the number of solutions for x^2-3x+6=0
2. Solve x^2+6x=0
3. Solve the following quadratic equation using the specified method. (5 points per solution method)
x^2+10x=3
A) Use the method of completing the square and square roots.
B) Use the Quadratic Formula.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

1. Use the discriminant to determine the number of solutions for
x%5E2-3x%2B6=0
b%5E2-4ac
%28-3%29%5E2-4%2A1%2A6
9-24
-15 => if discriminant%3C0 the quadratic equation will have no real solutions

2. Solve x%5E2%2B6x=0; factor
x%28x%2B6%29=0
solutions:
x=0 and
%28x%2B6%29=0->x=-6

3. Solve the following quadratic equation using the specified method. (5 points per solution method)
x%5E2%2B10x=3
A) Use the method of completing the square and square roots.
x%5E2%2B10x=3
%28x%5E2%2B10x%2Bb%5E2%29-b%5E2=3....since a=1 and 2ab=10->b=5
%28x%5E2%2B10x%2B5%5E2%29-5%5E2=3
%28x%2B5%29%5E2-25=3
%28x%2B5%29%5E2=3%2B25
%28x%2B5%29%5E2=28
sqrt%28%28x%2B5%29%5E2%29=sqrt%2828%29
x%2B5=sqrt%284%2A7%29
x%2B5=2sqrt%287%29
x=2sqrt%287%29-5
solutions:
x=2sqrt%287%29-5
x=-2sqrt%287%29-5
B) Use the Quadratic Formula.
x%5E2%2B10x=3
x%5E2%2B10x-3=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-10+%2B-+sqrt%2810%5E2-4%2A1%2A%28-3%29%29%29%2F%282%2A1%29+
x+=+%28-10+%2B-+sqrt%28100%2B12%29%29%2F2+
x+=+%28-10+%2B-+sqrt%28112%29%29%2F2+
x+=+%28-cross%2810%295+%2B-+cross%284%292sqrt%287%29%29%2Fcross%282%29+
x+=+%28-5+%2B-+2sqrt%287%29%29+
solutions:
x+=+-5+%2B+2sqrt%287%29+
x+=+-5+-+2sqrt%287%29+