Question:
Express x^2 + 4x in the form (x + a)^2 + b , stating the numerical values of a and b.
The functions f and g are defined as follows:
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(i) Show that the equation has no real roots.
(ii) State the domain of , and find an expression in terms of for .
(iii) Sketch, in a single diagram, the graph of and , making clear the relationship between these graphs.
Attempt:
,
I can't complete because I get a negative value in the square root. Where did I go wrong?
i hope you know the rules on real and imaginary roots:
ax^2 + b.x + c
if b^2 - 4.a.c > 0 you will have two different real roots
if b^2 - 4.a.c = 0 you will have equal real roots
if b^2 - 4.a.c < 0 you will have imaginary conjugate roots
in your case:
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.
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= (x+2)^2 +2
= x^2 + 4x +6 ====> a=1, b=4, c=6
b^2 - 4.a.c = -8 (two imaginary roots)
This is a tricky question. It turns out that you can also find the inverse function . But for the function
, the domain is , all of the numbers that will maintain a nonnegative value within the square root. The range for this function is , since the square root is always greater than or equal to zero. See if you can find the domain and range for the other inverse function.
Hello,
Discriminant - Wikipedia, the free encyclopedia
To sum up :
If you have an equation
If , the equation has no real root and is of the same sign as a.
If ,
If ,