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May 13th, 2015, 07:46 AM   #1
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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.
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May 13th, 2015, 10:42 AM   #2
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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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May 15th, 2015, 11:58 AM   #3
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Quote:
Originally Posted by skaa View Post
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:
$\displaystyle 8k+25<0$
$\displaystyle k<-\frac{25}{8}$
Thanks, I wish I gave that answer
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