Question 1

Wait, when Sal does the 4x^2= 52 example, he says that the solution is +√13 and -√13. If we plug in the -√13 into the original quadratic equation, doesn't the negative sign remain because it is outside the square root sign? So, isn't -√13 not a solution to the quadratic equation?

Accepted Answer

When you plug in a value for x, it behaves as if it were contained within parentheses for the purpose of order of operations. So 4x^2=52 becomes 4(-√13)^2 = 52, which in turn means 4 (-√13)(-√13) = 52. Since you square the entire -√13 expression, the negative cancels itself out, leaving you with 13.

What you are thinking about is something like -3^2, which is in fact -9, because order of operations suggests it is actually (-1)(3)^2 = (-1)(3)(3) = (-1)(9) = -9. If you were plugging -3 into an equation to replace x, such as x^2, then it would be evaluated as (-3)^2, or simply, 9.

Question 2

Wait, when Sal does the 4x^2= 52 example, he says that the solution is +√13 and -√13. If we plug in the -√13 into the original quadratic equation, doesn't the negative sign remain because it is outside the square root sign? So, isn't -√13 not a solution to the quadratic equation?

Accepted Answer

It is a solution because ( -√13 )^2 is 13 and 13*4 =52.

Question 3

Why positive or negative in the square root?

Accepted Answer

Well, if we start with 
`x² = 9`
we know that something times itself is 9
We know immediately that x can equal 3, because `3 x 3 = 9`
However, we have to put on the brakes here, because there is another way to get 9 by multiplying negative 3 by itself:
` -3 x -3 = 9`
Because of that, if we are solving x² = 9, we have to allow for either correct answer.
So we say, x = ± 3 and that means that x = 3  or x = -3

When we have the more complicated case of `x² = 13`
the square root will be x = ± √13  and that means we have two possible answers:
x = +√13 and x = - √13

You have to be careful, though, because if the problem says 
What is √16 , this only has one answer.  √16 means `give me the principal square root of 16` and that is asking for only the *positive* root.

Question 4

I thought you can't have a negative under the radical. I don't see how you can say "the square root of negative 13?"

Accepted Answer

It's not "the square root of negative 13", it's "the negative square root of 13".

For example, if you have 4, its positive square root is 2, its negative square root is -2.

Question 5

Why cant i just wake up with a 1500+ score

Accepted Answer

Because happiness has to be fought for.

Question 6

does equations that have x^2 always have 2 answers, what about ones with just x

Accepted Answer

You right! The equation x^2 would have two answers, because when you have something that is square rooted it has a positive and a negative root. X would only have one answer because it would be what ever X was. Try going to a online graphing calculator called Desmos and plug those in and you will see that it crosses the x axis twice for the first one and once or the second one.

Question 7

What is the difference between √13 and 13? I get that's it's a square root symbol but it doesn't make sense to me. Couldn't the answer also be -13 and 13 to this equation?

Accepted Answer

Not at all. √13 is roughly equal to 3.606 because when you square 3.606, you get 13. Squaring and taking the square root are inverse equations, squaring multiplies the number by itself, taking the square root gives you the number you would need to square to get that original number. 
Make sense?

Question 8

Why is there positive or negative in square root? why is it important to the equation?

Accepted Answer

When you take the square root of something, you're asking yourself: "What number would I have to multiply by itself to get this number that I'm taking the square root of". If you multiply any number by itself, regardless of whether its positive or negative, the answer will be a positive number. The squaring basically cancels out any negatives, so our solution set needs to reflect this by including the negative root. In general, whenever you take the square root of both sides of an equation to simplify an exponent, it is plus or minus.

Course: Digital SAT Math > Unit 4

Solving quadratic equations — Basic example

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