Let S be the set of all non-zero real numbers αsuch that the quadratic equation αx2-x+&#94

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Let S be the set of all non-zero real numbers &#945;such that the quadratic equation &#945;x2-x+&#945;=0= 0 has two distinct real roots x1 and x2 satisfying the inequality x1-x2&#60;1.1. Which of the following intervals is(are) a subset(s) of S

Accepted Answer

Here, 0&#60;(x1-x2)2&#60;1&#8658;0&#60;(x1+x2)2-4x1x2&#60;1&#8658;0&#60;1&#945;2-4&#60;1 &#8658;&#945;&#8712;-12,-15&#8746;15,12

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