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

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.

  • -3
What are you looking for?