4. If the roots of the quadratic equation (x-a) (x - b) +(x-b)(x-c) +(x-c)(x-a)= 0 are equal Then,
show that a = b = c.
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Given quadratic equation is
So, on comparing with Ax² + Bx + C = 0, we get
As it is given that, equation has real and equal roots.
can be rewritten as
Concept Used :-
Nature of roots :-
Let us consider a quadratic equation ax² + bx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.
If Discriminant, D > 0, then roots of the equation are real and unequal.
If Discriminant, D = 0, then roots of the equation are real and equal.
If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.
Where,
Discriminant, D = b² - 4ac
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