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If the equation x^2+ax+bc=0" and " x^2+b...

If the equation `x^2+ax+bc=0" and " x^2+bx+ca=0` have a common root, then `a+b+c` =

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  2. The set {R e((2i z)/(1-z^2)): z is a complex number , |z|=1,z=+-1} is...

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  3. If the equation x^2+ax+bc=0" and " x^2+bx+ca=0 have a common root, the...

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  4. If a r g["z"1("z"3-"z"2)]=a r g["z"3("z"2-"z"1)] , then prove that O ,...

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  5. If x" - "i y" "=sqrt((a-i b)/(c-i d)) prove that (x^2+y^2)^2=(a^2+b^2...

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  6. If x^3+3x^2-9x+c is of the form (x-alpha)^2(x-beta) , then c is equ...

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  7. If x=a+b,y=a alpha+b beta and z=abeta+ b alpha , where alpha and beta...

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  8. If z=(a+ib)^5+(b+ia)^5 then prove that Re(z)=Im(z), where a,b in R.

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  9. If a and b are positive numbers and eah of the equations x^2+a x+2b=0 ...

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  10. Find the real values of x and y for which the following equation is sa...

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  11. The three angular points of a triangle are given by Z=alpha, Z=beta,Z=...

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  12. Suppose a ,b ,c are the roots of the cubic x^3-x^2-2=0. Then the value...

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  13. It is given that n is an odd integer greater than 3 but n is not a mul...

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  14. If alpha,beta,gamma,delta are four complex numbers such that gamma/del...

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  15. If ax^(2)+(b-c)x+a-b-c=0 has unequal real roots for all c epsilon R, ...

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  16. If z1^2+z2^2+2z1.z2.costheta= 0 prove that the points represented by ...

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  17. Prove that the circles z bar z +z( bar a 1)+bar z( a1 )+b1=0 ,b1 in ...

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  18. If a , b ,c real in G.P., then the roots of the equation a x^2+b x+c=0...

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  19. If z0 is the circumcenter of an equilateral triangle with vertices z1,...

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  20. Two different non-parallel lines cut the circle |z| = r at points a...

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