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If x^2+ax+bc=0 and x^2+bx+ac=0 have a co...

If `x^2+ax+bc`=0 and `x^2+bx+ac`=0 have a common root, show their other root satisfies the equation `x^2+cx+ab`=0

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If x is real and (x^2+2x+c)/(x^2+4x+3c) can take all real values, of t...

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  2. Find the range of f(x)=sqrt(x-1)+sqrt(5-xdot)

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  3. If x^2+ax+bc=0 and x^2+bx+ac=0 have a common root, show their other ro...

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

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

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

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  7. Evaluate: i^(135) (-sqrt(-1))^(4n+3),n in N sqrt(-25)+3sqrt(-4)+...

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

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

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

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

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

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

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  14. Find the number of positive integral values of k for which kx ^(2) +(k...

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  15. If x^2+2ax+a lt 0 AA x in [1, 2] then find set of all possible values ...

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  16. Given that a ,b ,c are distinct real numbers such that expressions a x...

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  17. Find the number of quadratic equations, which are unchanged by squarin...

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  18. Solve the following: (sqrt(x^2-5x+6)+sqrt(x^2-5x+4))^(x/2)+(sqrt(x^2-...

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  19. Show that the equation A^2/(x-a)+B^2/(x-b)+C^2/(x-c)+.....+H^2/(x-h)=...

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  20. Find the values of a if x^2-2(a-1)x+(2a+1)=0 has positive roots.

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