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Vlad1618 [11]
3 years ago
15

Factor 9x2 + 25 over the set of complex numbers. Enter your answer in the box.

Mathematics
1 answer:
kogti [31]3 years ago
4 0
(3x+5i)(3x-5i)



9x^2+25
=(3x)^2 + (5)^2
=(3x+5i)(3x-5i)
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For which k are the roots of k(x2+1)=x2+3x–3 real and distinct?
Ugo [173]

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Step-by-step explanation:

we have

k(x^{2}+1)=x^{2}+3x-3

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x^{2}-kx^{2}+3x-3-k=0

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we know that

If the discriminant is greater than zero . then the quadratic equation has two real and distinct solutions

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substitute

D=3^{2}-4(1-k)(-3-k)\\ \\D=9-4(-3-k+3k+k^{2})\\ \\D=9+12+4k-12k-4k^{2}\\ \\D=21-8k-4k^{2}

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21-8k-4k^{2} > 0

solve the quadratic equation by graphing

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see the attached figure

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