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If x^2+p x+1 is a factor of the expressi...

If `x^2+p x+1` is a factor of the expression `a x^3+b x+c ,` then `a^2-c^2=a b` b. `a^2+c^2=-a b` c. `a^2-c^2=-a b` d. none of these

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  2. If a is a complex number such that |a|=1, then find the value of a, s...

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  3. If x^2+p x+1 is a factor of the expression a x^3+b x+c , then a^2-c^2=...

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  4. Find the value of expression (cospi/2+i sin(pi/2))(cos(pi/(2^2))+i si...

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  5. Solve for z , i.e. find all complex numbers z which satisfy |z|^2-2i z...

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  6. If alpha, beta are the roots of x^(2) - px + q = 0 and alpha', beta' a...

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  7. If a ,b are complex numbers and one of the roots of the equation x^2+a...

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  8. If |z1|=|z2|=1, then prove that |z1+z2|= |1/z1+1/z2∣

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  9. If (a x^2+c)y+(a^(prime)x^2+c^(prime) )=0 and x is a rational function...

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  10. Find the principal argument of the complex number sin(6pi)/5+i(1+cos(6...

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  11. For x in (0,1) , prove that i^(2i+3) ln((i^3x^2+2x+i)/(i x^2+2x+i^3))=...

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  12. The sum of the non-real root of (x^2+x-2)(x^2+x-3)=12 is -1 b. 1 c. -...

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  13. If n is a positive integer, prove that |I m(z^n)|lt=n|I m(z)||z|^(n-1....

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  14. The number of roots of the equation sqrt(x-2)(x^2-4x+3)=0 is (A) Thre...

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  15. If z1, z2a n dz3, z4 are two pairs of conjugate complex numbers, then ...

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  16. Prove that following inequalities: |z/(|z|)-1|lt=|a rgz| (ii) |z-1|lt=...

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  17. If x=1+i is a root of the equation =x^3-i x+1-i=0, then the other real...

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  18. Find the modulus, argument, and the principal argument of the complex ...

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  19. Find the principal argument of the complex number ((1+i)^5(1+sqrt(3i))...

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  20. Column I, Column II: possible argument of z=a+i b a b >0 , p. tan^(...

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