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![[Post New]](/templates/default/images/icon_minipost_new.gif) 13 Feb 2008 21:01:45 IST
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Q: If a,b,c = R and a+b+c = 0, then the quadratic equation 3ax2 + 2bx +c = 0 has; (multiple may be correct).
(A) at least one root in [0,1]
(B) at least one root in [-1,1]
(C) atleast one root in [0,2]
(D) none of these.
ans. given is a,b,c...can neone xplain??
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MaNuTd RoXxXx..MaNuTd 2 WiN PrEmIeR LeAgUe ThIs SeAsOn ToO AlOnG WiTh ChAmPiOnS LeAgUe.....HaiL RoNaLdO ...HaiL LaMpArD... |
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13 Feb 2008 21:11:04 IST
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Consider f(x) = ax3+bx2+cx we can see that x = 0 is a zero of f(x). also it is given that f(1) = a+b+c = 0. Hence x =1 is another zero. f'(x) = 3ax2+2bx+c by Rolle's theorem will therefore have a zero in the interval [0,1] which is a subset of the intervals in options (b) and (c). Hence, (a), (b) and (c) are all correct.
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Time wounds all heels |
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13 Feb 2008 21:14:16 IST
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hay hsbhatt f(1) is 3a+2b+c
and not a+b+c
so u canot say f(1)=0
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13 Feb 2008 21:16:20 IST
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iitjee08aspirant bhai , look at the soln properly
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13 Feb 2008 21:17:23 IST
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if f(x) = ax3+bx2+c then f(1) = a+b+c = 0 as given.
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