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If `alpha,beta,gamma` are the roots of he euation `x^3+4x+1=0,` then find the value of `(alpha+beta)^(-1)+(beta+gamma)^(-1)+(gamma+alpha)^(-1)` .

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If alpha,beta,gamma are the roots of the equation x^3+p x^2+q x+r=0, t...

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  2. Equations x^3+5x^2+p x+q=0a n dx^3+7x^2+p x+r=0 have two roots in com...

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  3. If alpha,beta,gamma are the roots of he euation x^3+4x+1=0, then find ...

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  4. If the roots of the equation x^3+P x^2+Q x-19=0 are each one more that...

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  5. If a ,b ,p ,q are non zero real numbers, then how many comman roots wo...

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  6. If x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) have a common roots, show that ...

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

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  8. If equations x^2+a x+12=0. x^2+b x+15=0a n dx^2+(a+b)x+36=0, have a co...

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

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

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

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

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

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

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

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

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  17. Solve the equation x(x+2)(x^2-1)=-1.

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  18. The number of distinct real roots of x^4 - 4 x^3 + 12 x^2 + x - 1 = 0...

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  19. Prove that graphs of y=x^2+2a n dy=3x-4 never intersect.

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  20. In how many points the line y+14=0 cuts the curve whose equation is x(...

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