SOLUTION: can you help me with these problems?? thank you so much 1.) {{{a^2-4a+3=0}}} 2.) {{{x^2-4x-10=0}}} 3.) {{{3b^2+4b-2=0}}} 4.) {{{2c^2+5c-2=0}}}

Question 197253: can you help me with these problems?? thank you so much
1.)
2.)
3.)
4.)
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first two to get you started...

# 1

Start with the given equation.

Notice we have a quadratic in the form of where , , and

Let's use the quadratic formula to solve for a

Start with the quadratic formula

Plug in , , and

Negate to get .

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

# 2

Start with the given equation.

Notice we have a quadratic in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

Break up the fraction.

Reduce.

or Break up the expression.

So the solutions are or

which approximate to or

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

1.)

This factors because and , so:

Use the Zero Product Rule:

or

2.) does not factor.

You can tell whether a quadratic will factor by computing the discriminant. The discriminant is the expression under the radical in the quadratic formula, namely . If the result is not a perfect square, then the quadratic does not factor over the rationals. Here you have -4 squared is 16 and 4 times 1 times -10 = -40 and 16 - (-40) is 56 which is not a perfect square.

Since the quadratic does not factor, you can either complete the square or use the much easier process of using the quadratic formula:

The other two do not factor either, proof of which is left as an exercise for the student. You do them the same way -- use the quadratic formula.

John

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