Statement Explanation?

Question

This tells use there is a quadratic with no real roots. So by moving the function down (by k) until it touches the x-axis (4 zeros shown (multiplicity of 2) )or the turning point is below the x-axis (5 zeros shown) you have created a function that one can see all roots. When you move the function down all the zeros will be moved also.

Can someone explain to me more briefly on that statement above, give me an example if you can so it will be more clearer.

what do you mean by a quadratic without any real roots? examples please!

Answer 1

If a quadratic has no real roots, it's graph will show that no part of it touches or crosses the x-axis. "Moving down" means adding a constant to the equation (negative if the curve lies entirely above the x-axis or positve if it lies below) until the curve touches the x-axis. If it just touches, the two roots of the equation are real and the same value. Adding more to move the curve so that it crosses the x-axis twice, means there are two different real roots. I don't know what the terms "4 zeros shown" or "5 zeros shown" means, since a quadratic has only two roots.

Answer 2

Just by using the formula to solve normal quadratic equation Ax^2 + Bx + C = 0, the formula is
x= 1/2[-B+ (B^2 - 4AC)^(1/2)] or
x= 1/2[-B - (B^2 - 4AC)^(1/2)]
The number of the roots of the equation can be defined simply by calculating (B^2 - 4AC)^(1/2), consider:
- If it's greater than 0, the equation has 2 distinctive roots
- It it's equal to 0, the equation has 2 equal roots
- If it's smaller than 0, the equation has no roots


OR if you use a graph, if the curve cuts the x-axis at 2 points, the eqn has 2 distinctive roots. If it touches the x-axis, it has 2 equal roots. If it doesnt touch the x-axis at all, the eqn doesnt have real root. It applies 4 both cases where A>0 or A<0. So by moving the curve (which means chaging the value of C), you can actually change the numbers of the eqn's roots. =) hope you got it clearly

Answer 3

the form is inaccurate. each condition in Hypertext Preprocessor might want to be enclosed in brackets. So: ==> if ( ($record == ".") || ($record == "..") || ($record == "index.Hypertext Preprocessor") ) The "." is the call of the muse, the ".." is the present listing call The "index.Hypertext Preprocessor" is he "homestead web page" of a Hypertext Preprocessor depending website. If $record is the muse, or $record is the present right now or $record is "index.Hypertext Preprocessor" => proceed (do not do something, bypass to the subsequent record contained in the listing.).