quadratic help

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if the equation ax² + bx + c = 0 does not have 2 distinct real roots and a + b > c, then prove that f(x) â‰¥ 0, for all x E R.

#Mathematics #Algebra

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5 Answers

36

rahul ·2011-10-28 09:02:33

let, f(x) = ax² + bx + c
now, since this equation dosen't have distinct real roots
so, D â‰¤ 0
=> b² - 4ac â‰¤ 0 or, a â‰¥ b²/4a --- (i)

and given, a > c - b

so can this help in proving a > 0

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36

rahul ·2011-10-28 11:29:09

will someone help me in this....?

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Shubhodip ·2011-10-28 23:56:39

No one will, if you post wrong questions ...

-(x^2 -x + 1)

it has no real root...a+b>c, (cuz a=-1,b=1,c= -1,so 0>-1)

But f(x)<0 for all real x, while you want us to prove f(x)â‰¥0, so its wrong...

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if you mean a+ c>b then the question is write, and it just means f(-1)>0 , so f(x)â‰¥0

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71

Vivek @ Born this Way ·2011-10-29 00:27:57

Sahi. I was lost.

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36

rahul ·2011-10-29 03:12:23

oh sorry.... a + c > b nt. a + b > c...... :P

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