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 May 13th, 2015, 07:46 AM #1 Newbie   Joined: Oct 2014 From: England Posts: 12 Thanks: 0 my exam question I had an exam today morning and I didn't answer this question because I can't even tell if it is inequalities or coordinate geometry 2x^2-x -3=k has no real roots. Find the set of possible values of k. May 13th, 2015, 10:42 AM #2 Senior Member   Joined: Mar 2011 From: Chicago, IL Posts: 214 Thanks: 77 Let's write this quadratic equation in standard form: $\displaystyle 2x^2-x-(k+3)=0$ The discriminant of it is: $\displaystyle 1+4(2)(k+3)=8k+25$ Quadratic equation has no real roots if the discriminant is lesser than 0: $\displaystyle 8k+25<0$ $\displaystyle k<-\frac{25}{8}$ May 15th, 2015, 11:58 AM   #3
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 Originally Posted by skaa Let's write this quadratic equation in standard form: $\displaystyle 2x^2-x-(k+3)=0$ The discriminant of it is: $\displaystyle 1+4(2)(k+3)=8k+25$ Quadratic equation has no real roots if the discriminant is lesser than 0: $\displaystyle 8k+25<0$ $\displaystyle k<-\frac{25}{8}$
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