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Show that the roots of the equation (a^(...

Show that the roots of the equation `(a^(2)-bc)x^(2)+2(b^(2)-ac)x+c^(2)-ab=0`
are equal if either `b=0` or `a^(3)+b^(3)+c^(3)-3acb=0`

Text Solution

Verified by Experts

Since the roots are equal
`:.D=0`
`implies4(b^(2)-ac)^(2)-4(a^(2)-bc)(c^(2)-ab)=0`
`implies(b^(2)-ac)^(2)-(a^(2)-bc)(c^(2)-ab)=0`
`=b(a^(3)-b^(3)+c^(3)-3abc)=0`
`impliesb=0` or `a^(3)+b^(3)+c^(3)-3abc=0`
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ARIHANT MATHS ENGLISH-THEORY OF EQUATIONS-Exercise (Subjective Type Questions)
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  13. If alpha, beta, gamma are the roots of the cubic x^(3)-px^(2)+qx-r=0 ...

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  14. If A(1),A(2),A(3),...,A(n),a(1),a(2),a(3),...a(n),a,b,c in R show that...

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