SOLUTION: Solve each quadratic equation. 1. 2x^2 - 3x - 11 = 0 2. 3x^2 + 48 = 0 3. 2x^2 - x + 1 = 0

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Solve each quadratic equation. 1. 2x^2 - 3x - 11 = 0 2. 3x^2 + 48 = 0 3. 2x^2 - x + 1 = 0       Log On


   

Question 256204: Solve each quadratic equation.
1. 2x^2 - 3x - 11 = 0
2. 3x^2 + 48 = 0
3. 2x^2 - x + 1 = 0
Found 2 solutions by drk, checkley77:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Solving 1 at a time, we get:
1. 2x^2 - 3x - 11 = 0
we can't factor, so we use the quadratic as
x+=+%283+%2B-+sqrt%289-4%2A2%2A%28-11%29%29%29%2F%284%29+
and we get
x+=+%283%2B-+sqrt%2891%29%29%29%2F4
--
2. 3x^2 + 48 = 0
divide by 3 to get
x%5E2%2B16=0
subtract 16 to get
x%5E2+=+-16
take a square root and we get
no solution
OR
+ or - 4i.
3. 2x^2 - x + 1 = 0
we can't factor this so we apply quadratic as
x+=+%281+%2B-+sqrt%281-4%2A2%2A1%29%29%2F%284%29
and we get
x+=+%281+%2B-+sqrt%28-7%29%29%2F%284%29
which has no solution or has imaginary roots.

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
1. 2x^2 - 3x - 11 = 0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=(3+-sqrt[-3^2-4*2*-11])/2*2
x=(3+-sqrt[9+88])/4
x=(3+-sqrt97)/64x=(3+-9.849)/6
x=(3+9.849)/4
x=12.849/4
x=3.2122 ans.
x=(3-9.849)/4
x=-6.849/4
x=-1.7122 ans.
2. 3x^2 + 48 = 0
3(x^2-16)=0
3(x+4)(x-4)=0
x+4=0
x=-4 ans
x-4=0
x=4 ans.
3. 2x^2 - x + 1 = 0
(2x+1)(x-1)=0
2x+1=0
2x=-1
x=-1/2 ans.
x-1=0
x=1 ans.