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Find the complete set of values of a such that `(x^2-x)//(1-a x)` attains all real values.

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If roots of a x^2+b x+c=0 are alphaa n dbetaa n d4a+2b+c >0,4a ,-2...

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  2. The equation (x/(x+1))^2+(x/(x-1))^2=a(a-1) has a. Four real roots ...

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  3. Find the complete set of values of a such that (x^2-x)//(1-a x) attain...

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  4. If alpha,beta are roots of x^2+p x+1=0a n dgamma,delta are the roots o...

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  5. If he roots of the equation12 x^2-m x+5=0 are in the ratio 2:3 then fi...

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  6. If alphaa n dbeta are the roots of x^2-a(x-1)+b=0 then find the value ...

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  7. The equation formed by decreasing each root of ax^(2)+bx+c=0 by 1 is2x...

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  8. If the sum of the roots of an equation is 2 and the sum of their cubes...

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  9. If x is real and (x^2+2x+c)//(x^2+4x+3c) can take all real values, of ...

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  10. If alpha,beta are the roots of the equation 2x^2+2(a+b)x+a^2+b^2=0 , t...

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  11. If x^2+a x+bc=0 a n d x^2+b x+c a=0(a!=b) have a common root, then pro...

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  12. Let alpha,beta are the roots of x^2+b x+1=0. Then find the equation wh...

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  13. Find the greatest value of a non-negative real number lambda for which...

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  14. If a ,b ,c in R such that a+b+c=0a n da!=c , then prove that the root...

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  15. If the fraction (x^3+(a-10)x^2-x+a-6)/(x^3+(a-6)x^2-x+a-10) reduces to...

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  16. If the equation (a-5)x^2+2(a-10)x+a+10=0 has roots of opposite sign, t...

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  17. If alphaa n dbeta are the roots of ax^2+bx+c=0a n dSn=alpha^n+beta^n,...

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  18. If alpha is a root of the equation 4x^2+2x-1=0, then prove that 4alp...

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  19. If both the roots of x^2-a x+a=0 are greater than 2, then find the val...

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  20. If (y^2-5y+3)(x ^2+x+1)<2x for all x in R , then fin the interval i...

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