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Prove that the roots of the equation `(a^4+b^4)x^2+4a b c dx+(c^4+d^4)=0` cannot be different, if real.

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CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If (a^2-1)x^2+(a-1)x+a^2-4a+3=0 is identity in x , then find the val...

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  2. Show that a real value of x will satisfy the equation (1-i x)//(1+i x)...

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  3. Prove that the roots of the equation (a^4+b^4)x^2+4a b c dx+(c^4+d^4)=...

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  4. If a+i b=((x+i)^2)/(2x^2+1), prove that a^2+b^2=((x^2+1)^2)/((2x^2+1)^...

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  5. If the roots of the equation x^2-8x+a^2-6a=0 are real distinct, then f...

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  6. Solve :z^2+|z|=0 .

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  7. If roots of equation x^2-2c x+a b=0 are real and unequal, then prove ...

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  8. Find the range of real number alpha for which the equation z+alpha|z-1...

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  9. If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, sho...

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  10. If (1+i)^2 /(3 - i) , then Re(z) =

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  11. Find the quadratic equation with rational coefficients whose one root ...

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  12. Let z be a complex number satisfying the equation (z^3+3)^2=-16 , then...

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  13. If f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c ,where ac!=0, then prove that f...

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  14. Find the real numbers x and y if (x-i y)(3+5i) is the conjugate of ...

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  15. If x is real, then x//(x^2-5x+9) lies between -1a n d-1//11 b. 1a n d-...

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  18. Find the real part of e^e^(itheta)

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  19. If alpha, beta and gamma are the roots of x^3 - x^2-1 = 0, then value ...

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  20. Prove that z=i^i, where i=sqrt-1, is purely real.

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