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If the roots of the equation a(b-c)x^2+b...

If the roots of the equation `a(b-c)x^2+b(c-a)x+c(a-b)=0` are equal, show that `2//b=1//a+1// c dot`

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CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
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  2. Find the range of real number alpha for which the equation z+alpha|z-1...

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

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

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

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  7. If P(x) = ax^2+bx+c, and Q(x) = -ax^2+dx+c, acne 0, then prove that P(...

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  8. Find the real numbers x and y if (x-iy)(3+5i) is the conjugate of -6-2...

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

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  10. Find the least positive integer n such that ((2i)/(1+i))^n is a positi...

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  11. Set of all real value of a such that f(x)=((2a-1)x^2+2(a+1)x+(2a-1))/(...

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  12. Find the real part of e^(ei theta)

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

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

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  15. If alpha,beta,gamma,delta are the roots of the equation x^4-K x^3+K x^...

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  16. In A B C ,A(z1),B(z2),a n dC(z3) are inscribed in the circle |z|=5. I...

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  17. Suppose that f(x) isa quadratic expresson positive for all real xdot I...

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  18. Multiply: (2+5i)(4-3i)

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  19. Let f(x)=ax^2-bx+c^2, b != 0 and f(x) != 0 for all x ∈ R. Then (a) ...

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

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