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The equation `x^3+5x^2+px+q`=0 and `x^3+7x^2+px+r`=0 have two roots in common. If their third roots be `gamma_1`and `gamma_2` respectively, then the ordered pair`(gamma_1,gamma_2)` is

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. In equation x^4-2x^3+4x^2+6x-21=0 if two its roots are equal in magn...

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  2. If alpha,beta,gamma are the roots of the equation x^3+p x^2+q x+r=0, t...

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  3. The equation x^3+5x^2+px+q=0 and x^3+7x^2+px+r=0 have two roots in com...

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

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

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

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  7. If x^2+p x+q=0a n dx^2+q x+p=0,(p!=q) have a common roots, show that 1...

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  8. a,b,c are positive real numbers forming a G.P. If ax^2+2bx+c=0and d...

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

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

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

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

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

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

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

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

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

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  19. The number of disitinct real roots of x^4-4x^3+12x^2+x-1=0 is

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

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