Maths Help!


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Hi,

i need help solving quadratic inequalities which cannot be factorised.

here are the question:

x^2 - 3x + 5 < 0

x^2 + 2x + 4 >0

x^2 - 4x - 4 <=0

x^2 - 6x + 1 >0

if you can guys can guide me in solving just one of them, i'm sure i can solve the rest....

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i could be wrong, but the quadratic formula should help here....

img9.gif

where in this case:

"x^2 - 3x + 5 < 0"

a = 1

b = -3

c = 5

substitute into the formula and there are the two solutions for x.

put them onto a number line to turn them back into inequalities...

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ok, i figured out how to do it....

for those interested, you have to complete the square:

x^2 - 3x + 5 < 0

(x - 3/2)^2 - 9/4 + 5 < 0

(x - 3/2)^2 + 11/4 < 0

since the graph is always above 0, there are no solutions. (if the sign is > instead, then the solution will be all real numbers)

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