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rozzy5132
19.08.2019 •
Mathematics
How do you solve a quadratic equation
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Ответ:
(3 – 3)(3 – 4) ?=? 0
(0)(–1) ?=? 0
0 = 0Checking x = 4 in (x – 3)(x – 4) = 0:([4] – 3)([4] – 4) ?=? 0
(4 – 3)(4 – 4) ?=? 0
(1)(0) ?=? 0
0 = 0So both solutions "check" and are thus verified as being correct.Solve x2 + 5x + 6 = 0.This equation is already in the form "(quadratic) equals (zero)" but, unlike the previous example, this isn't yet factored. The quadratic must first be factored, because it is only when you MULTIPLY and get zero that you can say anything about the factors and solutions. You can't conclude anything about the individual terms of the unfactored quadratic (like the 5x or the 6), because you can add lots of stuff that totals zero.So the first thing I have to do is factor:x2 + 5x + 6 = (x + 2)(x + 3)Set this equal to zero:(x + 2)(x + 3) = 0Solve each factor: Copyright © Elizabeth Stapel 2002-2011 All Rights Reservedx + 2 = 0 or x + 3 = 0
x = –2 or x = – 3The solution to x2 + 5x + 6 = 0 is x = –3, –2Checking x = –3 and x = –2 in x2 + 5x + 6 = 0:[–3]2 + 5[–3] + 6 ?=? 0
9 – 15 + 6 ?=? 0
9 + 6 – 15 ?=? 0
15 – 15 ?=? 0
0 = 0[–2]2 + 5[–2] + 6 ?=? 0
4 – 10 + 6 ?=? 0
4 + 6 – 10 ?=? 0
10 – 10 ?=? 0
0 = 0So both solutions "check".Solve x2 – 3 = 2x.This equation is not in "(quadratic) equals (zero)" form, so I can't try to solve it yet. The first thing I need to do is get all the terms over on one side, with zero on the other side. Only then can I factor and solve:x2 – 3 = 2x
x2 – 2x – 3 = 0
(x – 3)(x + 1) = 0
x – 3 = 0 or x + 1 = 0
x = 3 or x = –1Then the solution to x2 – 3 = 2x is x = –1, 3Solve (x + 2)(x + 3) = 12.It is very common for students to see this type of problem, and say:"Cool! It's already factored! So I'll set the factors equal to 12 and
solve to get x = 10 and x = 9. That was easy!"Yeah, it was easy; it was also (warning!) wrong. Besides the fact that (10 + 2)(9 + 3) does not equal 12, you should never forget that you must have "(quadratic) equals (zero)" before you can solve.So, tempting though it may be, I cannot set each of the factors above equal to the other side of the equation and "solve". Instead, I first have to multiply out and simplify the left-hand side, then subtract the 12 over to the left-hand side, and re-factor. Only then can I solve.(x + 2)(x + 3) = 12
x2 + 5x + 6 = 12
x2 + 5x – 6 = 0
(x + 6)(x – 1) = 0
x + 6 = 0 or x – 1 = 0
x = –6 or x = 1Then the solution to (x + 2)(x + 3) = 12 is x = –6, 1
Ответ:
The answer is option B.
g(x) = - x²
Hope this helps you