if the points(a2,a) and (3,-2) lie on opposite sides of the line x+y+1=0 then belongs to the interval.

Dear Student,
Please find below the solution to the asked query:

x+y+1=0Put x, y=3,-2 we get,3-2+1=2>0As given points lie on the opposite side, When we put a2,a in line we havea2+a+1<0 ; conditioniIn any quadratic function fx=px2+qx+rif p>0 and D=q2-4pr<0Then px2+qx+r>0 for all xRIn a2+a+1Coefficient of a2>0 and and D=1-4=-3<0a2+a+1>0 for all aRConditioni will not be satisfied for any value of a.Hence there exists no value of a for which a2,a and 3,-2lie on opposite side of line x+y+1=0

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