aisoku Posted January 12, 2004 Share Posted January 12, 2004 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.... Link to comment Share on other sites More sharing options...
**marisa** Posted January 12, 2004 Share Posted January 12, 2004 i could be wrong, but the quadratic formula should help here.... 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... Link to comment Share on other sites More sharing options...
aisoku Posted January 12, 2004 Author Share Posted January 12, 2004 i dont think it would work since this same way doesnt work when the inequalities are able to be factorised Link to comment Share on other sites More sharing options...
**marisa** Posted January 12, 2004 Share Posted January 12, 2004 k well i will solve it on paper and get back to you.... :) Link to comment Share on other sites More sharing options...
aisoku Posted January 13, 2004 Author Share Posted January 13, 2004 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) Link to comment Share on other sites More sharing options...
Recommended Posts