Chemistry miscellaneousHard

Question

Let S be the set of all non-zero real numbers αsuch that the quadratic equation αx2-x+α=0= 0 has two distinct real roots x1 and x2 satisfying the inequality x1-x2<1.1. Which of the following intervals is(are) a subset(s) of S

Options

A.

-12,-15

B.

-15,0

C.

0,15

D.

15,12

Solution

Here, 0<(x1-x2)2<1⇒0<(x1+x2)2-4x1x2<1⇒0<1α2-4<1
⇒α∈-12,-15∪15,12

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