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Find the values of `a` for which one root of equation `(a-5)x^(2)-2ax+a-4=0` is smaller than 1 and the other greater than 2.

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To solve the problem, we need to analyze the quadratic equation given by: \[ (a-5)x^2 - 2ax + (a-4) = 0 \] We want to find the values of \( a \) such that one root is less than 1 and the other root is greater than 2. ...
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ARIHANT MATHS ENGLISH-THEORY OF EQUATIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. Find the values of a for which one root of equation (a-5)x^(2)-2ax+a-4...

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  2. In the quadratic equation ax^2 + bx + c = 0. if delta = b^2-4ac and al...

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  3. Let S denote the set of all polynomials P(x) of degree lt=2 such th...

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  4. If the roots of x^2-b x+c=0 are two consecutive integers, then b^2-4c ...

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  5. If the equation a(n)x^(n)+a(n-1)x^(n-1)+..+a(1)x=0, a(1)!=0, n ge2, ha...

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  6. If both the roots of the quadratic equation x^(2)-2kx+k^(2)+k-5=0 are ...

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  7. Let aa n db be the roots of the equation x^2-10 c x-11 d=0 and those o...

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  8. Let a,b,c be the sides of a triangle. No two of them are equal and lam...

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  9. All the values of m for whilch both the roots of the equation x^2-2m x...

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  10. If the roots of the quadratic equation x^2+p x+q=0 are tan30^0a n dtan...

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  11. Let alpha,beta be the roots of the equation x^2-p x+r=0a n dalpha//2,2...

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  12. If the difference between the roots of the equation x^2+a x+1=0 is les...

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  13. Let a ,b , c ,p ,q be real numbers. Suppose alpha,beta are the roots o...

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  14. The quadratic equations x^2""-6x""+""a""=""0""a n d ""x^2""-c x""+""...

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  15. How many real solutions does the equation x^7+14 x^5+16 x^3+30 x-560=0...

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  16. Suppose the cubic x^(3)-px+q has three distinct real roots, where pgt0...

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  17. The smallest value of k, for which both the roots of the equation, x^2...

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  18. If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, t...

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  19. Let p and q real number such that p!= 0,p^3!=q and p^3!=-q. if alpha a...

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  20. solve 0=1+2x+3x^2

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  21. Find the roots of x^2-6x-2=0

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