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Find the values of the parameter a for w...

Find the values of the parameter a for which the roots of the quadratic equation `x^2+2(a-1)x+a+5=0` are
such that one root is greater than 3 and the other root is smaller than 1

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PATHFINDER-QUADRATIC EQUATION AND EXPRESSION-QUESTION BANK
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  4. Show that the equation A^2/(x-a)+B^2/(x-b)+C^2/(x-c)+.....+H^2/(x-h)=...

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  5. Solve the equation (x^2-6x)^2=81+2(x-3)^2

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  6. abs(x^2-3x-4)=9-abs(x^2-1)

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  7. Find the values of 'a' which 4^t-(a-4)2^t+9/4alt0,foralltin(1,2)

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  8. Find values of a for which the quadratic equation 3x^2+2(a^2+1)x+(a^2-...

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  9. For what real 'p' do the roots of x^2-2x-p^2+1=0 lie between the roots...

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  10. Ifax^2-bx+c=0 has two distinct roots lying in the interval (0,1),a,b,c...

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  11. Find the values of theta in the interval (-pi/2,pi/2) satisfying the e...

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  13. The equation x-2/(x-1)=1-2/(x-1) has

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  15. If alpha,beta,gamma are the roots of the equation x^3+x+1=0, then the ...

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  16. alpha,beta are the roots of the equation (a-2)x^2-(5-a)x-5=0.Find 'a' ...

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  17. If f(x) = g(x)^3+xh(x)^3 is divisible by x^2+x+1, then

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  18. If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal,the...

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  19. If the roots of the equation 6x^3-11x^2+6x-1=0 are in H.P., then the r...

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  20. A value of b for which the equations x^2+bx-1=0, x^2+x+b =0 have one r...

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