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Let a,b,c in R and a gt 0. If the quadr...

Let a,b,c ` in R and a gt 0`. If the quadratic equation ` ax^(2) +bx +c=0` has two real roots `alpha and beta` such that ` alpha gt -1 and beta gt 1` , then show that ` 1 + |b/a| + c/a gt 0`

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form the graph it is clear that ` f(-1) gt 0`
` f(1) gt 0`
` Rightarrow a -b +c gt 0 and a +b =c gt 0`
`Rightarrow a(1 -b/a +c/a)lt 0 and a(1+b/a+c/a) lt0`
` Rightarrow 1-b/a+c/a lt0 and 1 + b/a +c/a lt 0 " as " a lt 0`
` Rightarrow 1 + |b/a| + c/a gt 0`
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