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If a ,b ,c ,d in R , then the equation ...

If `a ,b ,c ,d in R ,` then the equation `(x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0` has a) 6 real roots b) at least 2 real roots c) 4 real roots d) none of these

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If the root of the equation (a-1)(x^2-x+1)^2=(a+1)(x^4+x^2+1) are real...

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  2. If alpha and beta are roots of the equation a x^2+b x+c=0, then the ro...

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  3. If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx...

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  4. Graph of y = f(x) is as shown in the following figure. Find th...

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  5. In how many points graph of y=x^3-3x^2+5x-3 intersect the x-axis?

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  6. The quadratic polynomial p(x) has the following properties:p(x)geq0 fo...

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  7. If (1-p) is a root of quadratic equation x^2+p x+(1-p)=0, then find it...

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  8. A polynomial in x of degree 3 vanishes when x=1 and x=-2 , ad has the ...

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  9. Let f(x)=a^2+b x+c where a ,b , c in R and a!=0. It is known that f(5...

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  10. If x=1 and x=2 are solutions of equations x^3+a x^2+b x+c=0 and a+b=1,...

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  11. If x in R ,a n da ,b ,c are in ascending or descending order of magni...

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  12. Prove that graphs y=2x-3 and y=x^2-x never intersect.

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  13. Which of the following pair of graphs intersect ? (i) y = x^(2) - x ...

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  14. If alpha and beta are the rootsof he equations x^2-a x+b=0a n dAn=alph...

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  15. If alpha,beta be the roots x^2+px-q=0 and gamma,delta be the roots of ...

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

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

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

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