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

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) (Show Source): You can put this solution on YOUR website!
# 10

Start with the given equation.

Notice that the quadratic is in the form of where , , and

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

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the solutions are or

# 42

Start with the given equation.

Subtract 24m from both sides.

Rearrange the terms.

From we can see that , , and

Start with the discriminant formula.

Plug in , , and

Square to get

Multiply to get

Subtract from to get

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

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