Math Homework Help?

Question

This makes no sence to me.. please help

Section 16.3: Let's look at problem #44. [Under what condition(s)
would using the quadratic formula not be the easiest way to solve a quadratic equation?] Explain, and find two problems: One that can be solved both by factoring and using the quadratic formula (do both ways) and one that cannot be solved by factoring.

Answer 1

ANY quadratic equation can be solved using the quadratic formula, but that's not always the easiest way to solve it. If you can factor a problem, that's almost always easier. An example of this would be x^2 + 13x + 42 = 0. Since you can easily find two numbers that multiply to give the constant (42) and add up to the linear term (13), this is easy to factor. Factoring the equation gives (x + 7)(x + 6) =0. The answers are the opposites of the factors, which would be -7 and -6. Using the quadratic formula, you'd have (-14 +or- SQR(13^2 - 4*1*42)) / 2, which is a lot more complicated.

Another time it's easier not to use the quadratic formula is if you have an equation with a perfect square, like (x + 3)^2 = 121. Just take the square root (and remember there are two answers). Here x + 3 = 11 or -11, so (subtracting 3) x would equal 8 or -14.