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If the expression a x^4+b x^3-x^2+2x+3 h...

If the expression `a x^4+b x^3-x^2+2x+3` has remainder `4x+3` when divided by `x^2+x-2,` find the value of `aa n dbdot`

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VIKAS GUPTA (BLACK BOOK) ENGLISH-QUADRATIC EQUATIONS -EXERCISE (SUBJECTIVE TYPE PROBLEMS)
  1. The number of all values of n, (whre n is a whole number ) for which t...

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  2. The number of negative intergral values of m for which the expression ...

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  3. If the expression a x^4+b x^3-x^2+2x+3 has remainder 4x+3 when divided...

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  4. The smallest value of k for which both roots of the equation x^(2)-8kx...

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  5. If x ^(2) -3x+2 is a factor of x ^(4) -px ^(2) +q=0, then p+q=

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  6. The expression x^2 + 2xy + ky^2 + 2x + k = 0 can be resolved into two ...

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  7. The curve y=(lambda=1)x^2+2 intersects the curve y=lambdax+3 in exactl...

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  8. Find the number of integral vaues of 'a' for which the range of functi...

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  9. When x ^(100) is divided by x ^(2) -3x +2, the remainder is (2 ^(k +1)...

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  10. Let p(x)=0 be a polynomial equation of the least possible degree, with...

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  11. The range of value's of k for which the equation 2 cos^(4) x - sin^(4...

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  12. Let p (x) be a polynomial with real coefficient and p (x)=x^(2)+2x+1. ...

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  13. Find the smallest positive integral values of a for which the greater ...

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  14. If the equation x ^(4)+kx ^(2) +k=0 has exactly two distinct real root...

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  15. Let P (x)=x ^(6) -x ^(5) -x ^(3) -x ^(2) -x and alpha, beta, gamma, de...

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  16. The number of integral value of a,a, in [-5, 5] for which the equation...

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  17. The number of non-negative integral vlaues of n, n le 10 so that a roo...

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  18. Let f (x) =ax ^(2) +bx+c, where a,b,c are integers and a gt 1. If f (x...

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  19. If x and y are real numbers connected by the equation 9x ^(2)+2xy+y^(2...

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  20. Consider two numbers a,b, sum of which is 3 and the sum of their cubes...

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