Flashcards
Quadratics
Cards in this deck (13)
- 1Completing the square of ax^2+bx+c=0 gives what?The quadratic formula
- 2Which part of the quadratic formula is known as the discriminant?b^2-4ac
- 3A positive discriminant (b^2-4ac>0) gives roots that are....Real and Different (distinct)
- 4If the discriminant is 0 (b^2-4ac=0) it gives roots that are....Equal / the same
- 5A negative discriminant (b^2-4ac<0) has....No solutions (in Further Maths they are known as imaginary)
- 6If p^2≥16, how would we express p?-4≤p≤4
- 7Complete the square for ax^2+bx+c(x+b/2)^2 +c-b^2/4
(this is not the quadratic formula because it isn't equal to 0) - 8What method would we use to solve a complex quadratic such as: (1-2x)^2+3(1-2x)-10=0 ?Assigning values, so (1-2x) = k
- 9How would you expand a cubic?Expand 2 brackets into a quadratic and then multiply the quadratic by the final bracket
- 10How would expand something like (x-1)^2(x+1)^2 ?Rewrite it as ((x-1)(x+1))^2 , expand the quadratic to (x^2)^2, and expand this to get x^4-2x^2+1
- 11How would we factorise x^3+6x^2+9x ?Factor out an x and factorise the quadratic
This method only works as x is a common factor - 12How would we factorise x^4-2x^2+1?Rewrite as the quadratic: (x^2)^2-2(x^2)+1
Assign (x^2) to k and factorise this to give: (k^2-1)(k^2-1)
This is equivalent to (k+1)(k+1)(k-1)(k-1) and therefore (k+1)^2(k-1)^2
This only works as we can create a quadratic - 13How would we complete the square for something like: 2x^2+16x-6 ?Factor out 2: 2(x^2+8x-3)
Complete square inside: 2((x+4)^2-19)
Multiply by 2: 2(x+4)^2 -38
(note how we leave the 2 outside the brackets, but multiply -19 by 2)
Information
- Description
- More advanced quadratic facts mainly consisting of completing the square
- Created by
- Doc Boff · Sep 2018
- Updated
- Dec 8, 2018
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