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LetP(x)=0 be the polynomial equation of ...

LetP(x)=0 be the polynomial equation of least possible degree with rational coefficients having `3sqrt7+3sqrt49` as a root. Then the product of all the roots of P(x)=0 is

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If the equations a x^2+b x+c=0 and x^3+3x^2+3x+2=0 have two common roo...

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  2. The value m for which one of the roots of x^2-3x+2m=0 is double of one...

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  3. LetP(x)=0 be the polynomial equation of least possible degree with rat...

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  4. The value of 'a' for which the equation x^3+ax+1=0 and x^4+ax^2+1=0, w...

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  5. If (mr ,1/mr) where r=1,2,3,4, are four pairs of values of x and y ...

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  6. If alpha,beta,gamma,sigma are the roots of the equation x^4+4x^3-6x^2+...

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  7. If tantheta1,tantheta2,tantheta3 are the real roots of the x^3-(a+1)x...

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  8. If roots of an equation x^n-1=0a r e1,a1,a2,..... a(n-1), then the v...

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  9. If alpha,beta are the roots of a x^2+b x+c=0,(a!=0) and alpha+delta,be...

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  10. Let f(x)=A x^2+B x+c ,w h e r eA ,B ,C are real numbers. Prove that if...

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  11. Let S be a square of unit area. Consider any quadrilateral which has o...

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  12. The real numbers x1, x2, x3 satisfying the equation x^3-x^2+b x+gamma=...

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  13. Let a,b,c be real. If ax^2+bx+c=0 has two real roots alpha,beta where ...

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  14. For alt=0 , determine all real roots of the equation x^2-2a|x-a|-3a^2=...

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  15. Solve for x :(5+2sqrt(6))^(x^2-3)+(5-2sqrt(6))^(x^2-3)=10.

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  16. If one root of the quadratic equation ax^2+bx+c=0 is equal to the n^th...

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  17. If a ,b ,c in R and equations a x^2+b x+c=0 and x^2+2x+3=0 have a com...

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  18. Find the condition that the expressions a x^2-b x y+c y^2a n da1x^2+b1...

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  19. If x^2+(a-b)x+(1-a-b)=0. where a ,b in R , then find the values of a ...

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  20. Let a ,b ,c be real numbers with a!=0 and alpha,beta be the roots of t...

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