How many real roots are there for the equation: xSQUARED + 3x - 1? IS THE ANSWER 2, 1, 4 OR 0, THNX FOR HELP?

Question

How many real roots are there for the equation: xSQUARED + 3x - 1?
2
1
4
0

Answer 1

Let's try the quadratic formula...

It says the roots are (-3 +/-sqrt(13))/2 Since 13 is positive, there are two real roots. If the thing inside the squareroot (b^2 - 4ac), called the "discriminant", is positive, there are two real roots. If it is negative, there is one real root. If it is negative, there are no real roots (but two complex ones).

Answer 2

1

Answer 3

I like Phineas' answer, but would like to expand on it a bit.

Remember, the roots of a quadratic are found with either the quadratic formula or doing the equivalent, which is completing the square. The formula:

[(neg B) +/- sqrt (some stuff)] / 2A

OK so far? The "some stuff" is called the "discriminant".

Now, in order for there to be ANY real roots, the discriminant has to be a non-negative number, right? If it's negative, there are no real numbers whose square is that negative number, so there are no real roots (and if you're using only real numbers as your domain, then there are no answers to the equation; the answers are complex numbers).

If the discriminant is positive, then there are two real answers, one obtained by adding the positive square root of the discriminant, and one obtained by adding its negative [thus +/- sqrt (D), got it?].

If the discriminant is zero, there is only one real root, because you add and subtract zero, giving the same answer.

There can never be more than two real roots to a quadratic equation. Remember what the roots represent when you plot the parabola that comes out of Y = AX^2 + BX + C is? The places where the parabola crosses the X-axis (where Y=0). There will either be no crossings (the parabola is entirely above the X-axis and concave upward, or entirely below and concave downward), one crossing (the "apex" of the parabola is tangent to the X-axis) or two (it crosses once on the way down and again on the way up).

So to get the number of roots, all you need do is determine whether the discriminant is positive, zero or negative (2, 1 and 0 real roots, respectively). Easy, right?

Answer 4

As James ok stated, there is one distinctive genuine root while the discriminant is 0. (and 2 while it somewhat is helpful, and none while it somewhat is unfavourable.) notice that he stated distinctive genuine root. each now and then the basis in this situation is talked approximately as a double root, so as that we are able to assert that the quadratic equation has 2 roots, because it somewhat is meant to. (they only take place to be equivalent subsequently.)

Answer 5

x = [- 3 ± √(9 + 4) ] / 2
x = [- 3 ± √13 ] / 2
This gives 2 roots and both are real numbers.
(i.e. are not complex numbers)