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Find all integral values of a for which ...

Find all integral values of a for which the quadratic expression `(x - a) (x - 10) + 1` can be factored as a product `(x + alpha) (x + beta)` of two factors and `alpha,beta in I.`

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A DAS GUPTA-Equations, Inequation and Expressions-Exercise
  1. If ax^2-bx + c=0 have two distinct roots lying in the interval (0,1); ...

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  2. The set of values of a for which the inequality, x^2 + ax + a^2 + 6a ...

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  3. Find all integral values of a for which the quadratic expression (x - ...

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  4. Find the values of the parameter a for which 4^x-a.2^x-a+3 <= 0 for at...

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  5. Find all values of the parameter a for which the inequality a.9^x +4(a...

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  6. Solve the equation sqrt(a(2x^x-2)+1)=1-2^x ,x in Rdot

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  7. Find the possible values of 'a' such that the inequality 3-x^(2)gt ...

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  8. The sum of all the integral value(s) of k in [0, 15] for which the ine...

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

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  10. If alpha,betaa n dgamma are roots of 2x 63+x^3-7=0 , then find the val...

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  11. If f(x)=x^2+b x^2+c x+da n df(0),f(-1) are odd integers, prove that f(...

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  12. If a, b, c are in GP, then the equations ax^2 +2bx+c = 0 and dx^2 +2ex...

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  13. Show that the minimum value of (x+a)(x+b)//(x+c)dotw h e r ea > c ,b >...

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  14. Find the values of a for which the expression (ax^2+3x-4)/(3x-4x^2+a) ...

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  15. If |(12x)/(4x^(2)+9)| le 1, then

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  16. Prove that for all real values of xa n dy ,x^2j+2x y+3y^2-6x-2ygeq-11.

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  17. The value(s) of m for which the expression 2x^2+mxy+3y^2-5y-2 can be ...

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  18. if alpha is a real root of the quadratic equation ax^2+bx+c=0 and beta...

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  19. If a1x^3 + b1x² + c1x + d1 = 0 and a2x^3 + b2x^2+ c2x + d2 = 0 have a ...

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  20. If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has at...

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