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The number of distinct real roots of ` x^4 - 4 x^3 + 12 x^2 + x - 1 = 0` is :

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Solve sqrt(x-2)(x^2-4x-5)=0.

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

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

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

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

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  6. Consider the graph of y = f(x) as shown in the following figure. ...

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  7. If x^2+p x-444p=0 has integral roots where p is prime number, then fin...

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  8. The equation a x^2+b x+c=0 has real and positive roots. Prove that th...

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  9. If the roots of the equation x^2-ax+b=0y are real and differ b a quan...

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  10. If (a x^2+b x+c)y+(a^(prime)x^2+b^(prime)x^2+c^(prime))=0 and x is a r...

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  11. Show that the minimum value of (x+a)(x+b)//(x+c) where a > c ,b > c , ...

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  12. Let a ,b in N and a > 1. Also p is a prime number. If a x^2+b x+c=p f...

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  13. If 2x^2-3x y-2y^2=7, then prove that there will be only two integral p...

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  14. If a and c are odd prime numbers and a x^2+b x+c=0 has rational roots ...

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  15. If f(x)=x^3+b x^2+c x+d and f(0),f(-1) are odd integers, prove that f...

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  16. If x is real, then the maximum value of y=2(a-x)(x+sqrt(x^2+b^2))

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  17. If equation x^4-(3m+2)x^2+m^2=0(m >0) has four real solutions which ar...

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  18. Number of positive integers x for which f(x)=x^3-8x^2+20 x-13 is a pri...

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  19. If set of values a for which f(x)=a x^2-(3+2a)x+6, a!=0 is positive fo...

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  20. Polynomial P(x) contains only terms of aodd degree. when P(x) is divid...

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