If one root of the quadratic equation a x2-b x-c-0 is the square of the other show that b 3-a 2 c-a c 2-3 a b c

Let nbsp;α nbsp;and nbsp;β nbsp;be nbsp;the nbsp;roots nbsp;of nbsp;the nbsp;quadratic nbsp;equation nbsp;ax2+bx+c=0.Then, nbsp;α+β= baa ...

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Nature of Roots

If one root o...

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If one root of the quadratic equation ax² + bx + c = 0 is the square of the other show that $b^{3} + a^{2} c + a c^{2} = 3 a b c$

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If one of the roots of equation:

ax²+bx+c=0

be the square of other ,show that

b³+a²c+ac²=3abc

a x^{2} + b x + c = 0

b^{3} + a^{2} c + a c^{2}

a x^{2} + b x + c = 0

b^{3} + a c^{2} + a^{2} c

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

i = \frac{a c^{2} - 6 a b c}{8 b^{3} - a^{2} c}

i = \sqrt{- 1}

a > b > c

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

a x^{2} + b x + c = 0

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