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Let `alpha+ibeta;alpha,beta in R ,` be a root of the equation `x^3+q x+r=0; q ,r in Rdot` A real cubic equation, independent of `alpha&beta,` whose one root is `2alpha` is (a)`x^3+q x-r=0` (b) `x^3-q x+4=0` (c)`x^3+2q x+r=0` (d) None of these

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  9. If a ,b ,p ,q are non zero real numbers, then how many comman roots wo...

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  11. a,b,c are positive real numbers forming a G.P. ILf ax^2+2bx+c=0...

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  13. If x is real and the roots of the equation a x^2+b x+c=0 are imaginary...

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  14. Solve (x^2+2)^2+8x^2=6x(x^2+2)

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  15. Find the value of 2+1/(2+1/(2+1/(2+oo)))

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  16. If both the roots of a x^2+a x+1=0 are less than 1, then find the exha...

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  17. If both the roots of x^2+a x+2=0 lies in the interval (0, 3), then fin...

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  18. Solve (x^2+3x+2)/(x^2-6x-7)=0.

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  19. Solve sqrt(x-2)+sqrt(4-x)=2.

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  20. Solve sqrt(x-2)(x^2-4x-5)=0.

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