Curve Sketching Urgent Help Please !??!?

Please can someone give me a step by step to solving this. I have no clue what this question is. I have several more like this and I'm doing them for my own benefit to improve. So if you could use the following question as an example so I can learn from it to do all the others. I will greatly appreciate any help and thanks in advance to anyone who does.

Question:

Show that the equation x^2 + (k-2)x -4 = 0 has real and distinct roots for all values of K

Please can someone give me a step by step to solving this. I have no clue what this question is. I have several more like this and I'm doing them for my own benefit to improve. So if you could use the following question as an example so I can learn from it to do all the others. I will greatly appreciate any help and thanks in advance to anyone who does.

Question:

Show that the equation x^2 + (k-2)x -4 = 0 has real and distinct roots for all values of K

Have you learnt about the discriminant? What happens when $b^2-4ac > 0$?

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There are two real solutions?

Cool so what happens when you sub in the coefficients of the quadratic equation?

You need to use the discriminant (as described above).

When the discriminant > 0, there are 2 distinct, real solutions.
When it = 0, you get a repeated root
When it < 0, you get no real roots at all (you get imaginary roots instead but you don't have to worry about them... for now...)



Regardless of the value of k, the discriminant k^2 - 4k + 20 is always going to be greater than 0. So, we can conclude that there are two real roots.

Here's a link: http://regentsprep.org/regents/math/algtrig/ate3/discriminant.htm

Hope this helps

You need to use the discriminant (as described above).

When the discriminant > 0, there are 2 distinct, real solutions.
When it = 0, you get a repeated root
When it < 0, you get no real roots at all (you get imaginary roots instead but you don't have to worry about them... for now...)



Regardless of the value of k, the discriminant k^2 - 4k + 20 is always going to be greater than 0. So, we can conclude that there are two real roots.

Here's a link: http://regentsprep.org/regents/math/algtrig/ate3/discriminant.htm

Hope this helps

You need to use the discriminant (as described above).

...

Hope this helps

Please can someone give me a step by step to solving this. I have no clue what this question is. I have several more like this and I'm doing them for my own benefit to improve. So if you could use the following question as an example so I can learn from it to do all the others. I will greatly appreciate any help and thanks in advance to anyone who does.

Question:

Show that the equation x^2 + (k-2)x -4 = 0 has real and distinct roots for all values of K

This is related to the discriminant. As it says the equation has 'real and distinct' roots, it means that it will have two different roots. By looking at the equation, it is apparent that it's a quadratic equation. So, the form of it is ax^2 + bx + c = 0. In this case, a = 1, b = k-2 and c = -4

For the equation to have two real and distinct solutions or roots, the discriminant (b^2 - 4ac) will have to be greater than (>) 0.

So, you have to show the discriminant is greater than 0 by substituting the values of a, b and c into the discriminant.


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You're only a few hours late...

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