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Let a ,b ,c be real. If a x^2+b x+c=0 ha...

Let `a ,b ,c` be real. If `a x^2+b x+c=0` has two real roots `alphaa n dbeta,w h e r ealpha<<-1a n dbeta>>1` , then show that `1+c/a+|b/a|<0`

Text Solution

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Let ` f(x) = x^(2) + (b)/(a) x + (c)/(a)` .
Accounting to the questions, we have the following graph.
From the graph.
` f(-1) lt 0 and f(1) lt 0`
`rArr 1 + (c)/(a) - (b)/(a) lt 0 and 1 + (c)/ (a) + (b)/(a) lt 0`

`rArr 1 + (c)/(a) + |(b)/(a)|lt 0` .
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