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Nature of Roots

If the roots ...

Question

If the roots of the equation $(c^{2} - a b) x^{2} - 2 (a^{2} - b c) x + b^{2} - a c = 0$ are equal, prove that either a = 0 or a³ + b³ + c³ = 3abc.

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Solution

The given quadric equation is, and roots are equal.

Then prove that either or

Here,

As we know that

Putting the value of

The given equation will have real roots, if

So, either

Hence

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Similar questions

c^{2} \neq a b

, and the root of

(c^{2} - a b) x^{2} - 2 (a^{2} - b c) x + (b^{2} - a c) = 0

are equal then show that

a^{3} + b^{3} + c^{3} = 3 a b c

If the roots of the equation $(c^{2} - a b) x^{2} - 2 (a^{2} - b c) x + (b^{2} - a c) = 0$ are real ane equal, show that either $a = 0 o r (a^{3} + b^{3} + c^{3}) = 3 a b c$ .

Q. If a+b+c=0, then the roots of the equation

(c^{2} - a b) x^{2} - 2 (a^{2} - b c) x + (b^{2} - a c) = 0

a^{3} + b^{3} + c^{3} - 3 a b c = 0

then the roots of the equation

(a^{2} - b c) x^{2} + 2 (b^{2} - a c) x + c^{2} - a b = 0

If the roots of the equation (csq-ab) xsq-2(asq-bc)x+bsq-ac=0 are equal prove that a=0 /a cube +b cube+c cube=3abc

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