Can anyone do this trial question? (1 Viewer)

[lolmb]

At least one zero of P(x)=3x^3 + px^2 + 15x + 10 is purely imaginary and p is real. Find p and hence write P(x) as a product of linear factors.

Thank You!

 

[seventhroot]

Use the sum and product of roots

 

[HeroicPandas]

At least 1 root is imaginary, so by the conjugate root theorem, it's conjugate is also a root

Let z be a purely imaginary root

Roots = ib, ib(conj), something

sum of roots = -p/3 = real

so, ib + ib(conj)+ something = real

ib - ib+ something = real

something = real

So roots are: imaginary, conjugate of imaginary and real

So roots are: ib, -ib, c

 

[integral95]

At least one zero of P(x)=3x^3 + px^2 + 15x + 10 is purely imaginary and p is real. Find p and hence write P(x) as a product of linear factors.

Thank You!

lel

the complex roots are purely imaginary, so they're simply in the form bi ,-bi (b is real)

 

[HeroicPandas]

oh yeh woops lol

 

[Amundies]

integral95, you missed an "i" in the final bracket