Quadratic EquationEasy
Question
x1 and x2 are the roots of equation ax2 + bx + c = 0 (Where a, b, c ∈ R) and x1x2 < 0, then roots of the equation x1(x - x2)2 + x2(x - x1)2 = 0 are :-
Options
A.Real and of opposite sign
B.Negative
C.Positive
D.Non-real
Solution
x2(x1 + x2) - 4x x1x2 + x1x2(x1 + x2) = 0
D = 16 x12x22 - 4x1x2(x1 + x2)
D > 0
So roots are real
and product of roots of the equation is negative
=
b′coz x1x2 < 0
so roots are real and opposite in sign.
D = 16 x12x22 - 4x1x2(x1 + x2)
D > 0
So roots are real
and product of roots of the equation is negative
=
b′coz x1x2 < 0
so roots are real and opposite in sign.
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