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Theorem : Let alpha, beta be the real ro...

Theorem : Let `alpha, beta` be the real roots of `ax^(2)+bx+c=0 and alpha lt beta`. Then
(i) `x in R, alpha lt x lt beta rArr ax^(2) + bx +c and 'a'` have opposite signs.
(ii) `x in R, x lt alpha" or "x gt beta rArr ax^(2) + bx+c` and 'a' have the same sign.

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Verified by Experts

The correct Answer is:
`therefore x in R, x lt alpha" or "x gt beta`
`rArr ax^(2) +bx+c and a` have the same sign.
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