Find the condition on the complex constant - - if z2-z- -0 has real roots-

The condition #160; is α^2 4β≥ 0 ...

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Complex Numbers

Find the cond...

Question

Find the condition on the complex constant $α, β$ if $z^{2} + z α + β = 0$ has real roots.

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Let $α, β$ be real and z be a complex number. If $z^{2} + α z + β = 0$ has two distinct roots on the line Re(z) = 1, then it is necessary that

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α, β

x^{2} + α z + β = 0

α

β

z

x^{2} + α z + β = 0

R e (x) = 1

α

β

α^{2} + β^{2} + α β = 0

If a>0 and the equation $a x^{2} + b x + c = 0$ has two real roots $α$ and $β$ such that $| α | \leq 1, | β | \leq 1,$ then

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