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If the equation x^(3)+ax^(2)+b=0 (b ne 0...

If the equation `x^(3)+ax^(2)+b=0 (b ne 0)` has a double root then

A

`a^(2)+2b=0`

B

`a^(2)-2b=0`

C

`4a^(3)+27b+1=0`

D

`4a^(3)+27b=0`

Text Solution

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The correct Answer is:
C
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ML KHANNA-THEORY OF QUADRATIC EQUATIONS -Problem Set - 3
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  2. If A={x:f (x) =0} and B ={x: g(x) =0}," then "A cap B will be the set ...

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  3. The quadratic equation x^(2) + (a^(2) - 2) x - 2a^(2) and x^(2) - 3x +...

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  4. If the equation ax^(2)+bx+c=0 and cx^(2)+bx+a=0 a ne c, have negative ...

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  5. The value of a so that the equations (2a-5) x^(2)-4x-15=0 and (3a-8) x...

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  6. If the equations ax^(2)+bx+c=0 and x^(2)+x+1=0 have a common root, the...

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  7. If the equations ax^(2)+bx+c=0 ,where a,b,c in R, a!=0 and x^(2)+2x+3=...

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  8. If the equations x^(2) - ax + b = 0 and x^(2) + bx - a = 0 have a comm...

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  9. If the quadratic equation x^(2) +ax +b =0 and x^(2) +bx +a =0 (a ne b...

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  10. If p,q,r are three distinct real numbers, p ne 0 such that x^(2)+qx +p...

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  11. If the quadratic equations, a x^2+2c x+b=0a n da x^2+2b x+c=0(b!=c) ha...

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  12. If every pair from among the equations x^(2)+ax+bc=0, x^(2)+bx+ca=0 an...

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  13. If the equations a x^2+b x+c=0a n dx^3+3x^2+3x+2=0 have two common roo...

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  14. If the equation x^(3)+ax^(2)+b=0 (b ne 0) has a double root then

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  15. If both the roots of k(6x^(2)+3)+rx+2x^(2)-1=0 and 6k(2x^(2)+1)+px+4x^...

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  16. alpha(1),beta(1) are the roots of ax^(2)+bx+c=0 and alpha(2), beta(2) ...

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  17. If a,b,c are in A.P. and if (b-c) x^(2)+(c-a) x+(a-b)=0 and 2 (c+a) x^...

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  18. If a x^2+b x+c=0a n db x^2+c x+a=0 have a common root and a, b, and c ...

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  19. If the equation x^(2)-px+q=0 and x^(2)-ax+b=0 have a comon root and th...

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  20. If the equation x^(3) - 3x + a = 0 has distinct roots between 0 and 1,...

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