SOLUTION: Using the formula. Solve each equation by using the quadratic formula #10: x^2 + 4x + 3 = 0 Number of Solutions #42: Find b^2 - 4ac and the number of real solutions to eac

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Using the formula. Solve each equation by using the quadratic formula #10: x^2 + 4x + 3 = 0 Number of Solutions #42: Find b^2 - 4ac and the number of real solutions to eac      Log On


   

Question 211327This question is from textbook Elementary and Intermediate Algebra, 3e
: Using the formula. Solve each equation by using the quadratic formula
#10: x^2 + 4x + 3 = 0
Number of Solutions
#42: Find b^2 - 4ac and the number of real solutions to each
equation.
9m^2 + 16 = 24m This question is from textbook Elementary and Intermediate Algebra, 3e

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 10



x%5E2%2B4x%2B3=0 Start with the given equation.


Notice that the quadratic x%5E2%2B4x%2B3 is in the form of Ax%5E2%2BBx%2BC where A=1, B=4, and C=3


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%284%29+%2B-+sqrt%28+%284%29%5E2-4%281%29%283%29+%29%29%2F%282%281%29%29 Plug in A=1, B=4, and C=3


x+=+%28-4+%2B-+sqrt%28+16-4%281%29%283%29+%29%29%2F%282%281%29%29 Square 4 to get 16.


x+=+%28-4+%2B-+sqrt%28+16-12+%29%29%2F%282%281%29%29 Multiply 4%281%29%283%29 to get 12


x+=+%28-4+%2B-+sqrt%28+4+%29%29%2F%282%281%29%29 Subtract 12 from 16 to get 4


x+=+%28-4+%2B-+sqrt%28+4+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-4+%2B-+2%29%2F%282%29 Take the square root of 4 to get 2.


x+=+%28-4+%2B+2%29%2F%282%29 or x+=+%28-4+-+2%29%2F%282%29 Break up the expression.


x+=+%28-2%29%2F%282%29 or x+=++%28-6%29%2F%282%29 Combine like terms.


x+=+-1 or x+=+-3 Simplify.


So the solutions are x+=+-1 or x+=+-3




# 42


9m%5E2%2B16=24m Start with the given equation.


9m%5E2%2B16-24m=0 Subtract 24m from both sides.


9m%5E2-24m%2B16=0 Rearrange the terms.


From 9m%5E2-24m%2B16 we can see that a=9, b=-24, and c=16


D=b%5E2-4ac Start with the discriminant formula.


D=%28-24%29%5E2-4%289%29%2816%29 Plug in a=9, b=-24, and c=16


D=576-4%289%29%2816%29 Square -24 to get 576


D=576-576 Multiply 4%289%29%2816%29 to get %2836%29%2816%29=576


D=0 Subtract 576 from 576 to get 0


Since the discriminant is equal to zero, this means that there is one real solution.