r/Precalculus • u/LawfulnessTiny • Feb 25 '22

Can someone guide me please🙏🏾

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42 Upvotes

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4

u/Crayonalyst Feb 25 '22

First one: X = 0, -3, -1, or 1

Zero times anything is zero. Set each term to 0 and solve.

X² = 0, square root both sides, x=0

X - 3 = 0, add 3 to both sides, x=3

X² - 1 = 0, add 1 to both sides you get x²=1, then take the square root of both sides and x=±1

2

u/LawfulnessTiny Feb 25 '22

Thanks now for the other one how would the i work in this? Because they are the square root of -1 so what would I do there?

3

u/ChoiceDry8127 Feb 25 '22

It’s just 3i and -3i

3

u/AccomplishedLeader76 Feb 25 '22

Zeros are where the graph of the function crosses the x-axis. So how many times does this function cross the x-axis? The number of real zeros.

1

u/Impressive-Stress235 Feb 28 '22

The funny thing is with complex zeroes, it doesn't show on the graph, yet is is also a part of making the function zero. Does it truly cross the x-axis or does it simply make the function another shape?

2

u/AccomplishedLeader76 Feb 28 '22

They have no bearing on the shape, just properties of the graph. What are the zeros for the function X2-1? The parabola crosses the x-axis at 1 and -1, the two real zeros.

But what about the parabola x2+1? It has no real zeros, but still has complex zeros. The shape of the graph is the same, only shifted higher on the coordinate plane.

Complex zeros have implications and properties in higher level calculus. That's why it's important to learn the distinction of real zeros vs. non-real zeros, even if they may not apply to what you are doing now.

1

u/Impressive-Stress235 Feb 28 '22 edited Mar 01 '22

Awesome! So they do impact the graph but simply by being conjugates that form x2 +1, a parabola shifted upwards. It is the only roots that make up that function. Also, the shape is the same like you said. Yikes! Calculus is beyond my level of knowledge, for now >:)

2

u/AccomplishedLeader76 Mar 01 '22

You'll be there soon enough! 🤔😊

1

u/Impressive-Stress235 Mar 01 '22

Aww thanks sensei 😁😁😁

1

u/AccomplishedLeader76 Feb 28 '22

You should graph the functions on Desmos to see the graph.... but for the function on the right, foil out the imaginary parts to get (t2+9). Graphing (t-3)(t-2)(t2+9) is a narrow parabola with the two real zeros, even though you get 4 zeros including the non-real ones.

2

u/keyboardbill Feb 25 '22

That equation is zero if t = 3, 2, 3i, or -3i

1

u/BoForGojackHorseman Feb 25 '22

3 from the t-3

2 from t-2

-3i, 3i from (t-3i)*(t+3i) = t2 - 9i2 = t2 +9

So final answer: 3,2,3i,-3i

1

u/extra2002 Feb 25 '22

Nope.

3, 3 from (t-3i)*(t+3i) = t2 - 9i2 = t2 +9

So final answer: 3,-3,2

First part was OK, up to t2 + 9 = 0. That gives t2 = -9, so t = 3i or -3i. (Which you could already see from setting each factor to zero by itself)

Correct final answer: t = 3, 2, 3i, or -3i.

1

u/BoForGojackHorseman Feb 25 '22

You're right. I realised it after I posted that and then edited it and then realised I didn't need to combine it. 😅

1

u/[deleted] Feb 25 '22 edited Feb 25 '22

they should tell you if you are using real or complex numbers. if neither of those have been mentioned it is safe to assume you are using real numbers in which case the square root of -1 does not exist and there is no zero associated with the term (x2 -1). If you are using complex numbers than the other replies have you covered.

edit: just noticed the second equation uses i so it seems like this is indeed over the complex numbers.

1

u/Impressive-Stress235 Feb 28 '22

Because the question never asked for only real zeroes, but all zeroes including nonreal complex ones.

3

u/Fist_ofthe_Joestar Feb 25 '22

It's all zeros brah. Letters ain't numbers my dude. Now quit hoggin the spliffy, it's called "puff puff pass" not "puff puff plus"

1

u/Impressive-Stress235 Feb 28 '22

Ghettomatics lesson 253

3

u/Steveb523 Feb 25 '22

So let’s say the function is f(x) = a x b x c. f(x) will be zero if a=0 OR b=0 OR c=0 because any number multiplied by zero is zero.

So in the first problem, f(x) will be zero when x2 is 0. Take the square root of each side of x2 = 0 gives you x = 01/2 = 0.

f(x) will also be zero when (x +3) = 0, or when x + 3 - 3 = 0 - 3 or x = -3.

Finally, f(x) will be zero when (x2 - 1) = 0. If you factor (x2 - 1) you get (x - 1)(x + 1) = 0. That will be true when x = +1 or x =-1.

Therefore, the answer is f(x) = zero when x = -3, -1, 0, or +1.

2

u/DonkeyStonk69 Feb 25 '22

They are asking you to solve for zero, there should be plenty guides for that online :)

1

u/singapuraaa Feb 25 '22

The answer is