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If b^2<2a c , then prove that a x^3+b x...

If `b^2<2a c` , then prove that `a x^3+b x^2+c x+d=0` has exactly one real root.

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Find the greatest and the least value of |z1+z2| ifz1=24+7ia n d|z2|=6...

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  2. If the complex numbers x and y satisfy x^3-y^3=98 ia n dx-y=7i ,t h e ...

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  3. If b^2<2a c , then prove that a x^3+b x^2+c x+d=0 has exactly one re...

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  4. If z is any complex number such that |z+4|lt=3, then find the greatest...

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  5. If z1, z2 and z3, are the vertices of an equilateral triangle ABC suc...

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  6. If two roots of x^3-a x^2+b x-c=0 are equal in magnitude but opposite ...

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  7. For any complex number z find the minimum value of |z|+|z-2i|

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  8. The greatest positive argument of complex number satisfying |z-4|=R e(...

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  9. If alpha,betaa n dgamma are the roots of x^3+8=0 then find the equat...

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  10. Prove that the distance of the roots of the equation |sintheta1|z^3+|s...

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  11. Let z1a n dz2 be two distinct complex numbers and let z=(1-t)z1+t z2 f...

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  12. If alpha,beta,gamma are the roots of the equation x^3-p x+q=0, then ...

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  13. If |z1-1|lt=1,|z2-2|lt=2,|z(3)-3|lt=3, then find the greatest value o...

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  14. Let w = (sqrt 3 + iota/2) and P = { w^n : n = 1,2,3, ..... }, Further ...

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  15. If the roots of equation x^3+a x^2+b=0a r ealpha1,alpha2 and alpha3(a ...

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  16. If z is a complex number, then find the minimum value of |z|+|z-1|+|2z...

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  17. Let |z|=2and w=(z+1)/(z-1),where z ,w , in C (where C is the set of c...

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  18. If alpha,betaa n dgamma are roots of 2x^3+x^2-7=0 , then find the va...

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  19. if z is complex no satisfies the condition | Z |>3. T...

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  20. If alpha is the nth root of unity, then 1+2alpha+3alpha^2+ ton terms e...

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