The polynomial P(x) = x^3 - 2x^2 + kx + 24 has roots a , b and γ
(i) It is known that two of the roots are equal in magnitude but opposite in sign.
Find the third root and hence find the value of k
Can you please help .
Stacey Warren - Expert brainly.com
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just having a bad day
how is 3rd root 2 ?
lols , having a bad day ? why ?
I passed the entry test to uni, but apparently, I need to get minimum of 2 A levels to get into it. A levels take 2 years to get. I have 4 months.
ohh ok LOL
I got so far (for roots a,-a and c)
3a +c = 2 and
a^2 c = 24
U get that?
w8 , what's c ?
I don't mean understand, I mean u calculated same?
I said for roots, a,-a and c
ohh lols , i dnt even know how to do it
There is similar (not same) formula like Vieta for cubic as for quadratic....
What's Vieta ?
Formulae for sum and product of roots of quadratic.
Let a be the first root >0. Then b=-a
Now since a cubic function with 3 real roots then must be of the form:
(x-a)(x-b)(x-v)= x^3 - 2x^2 + kx + 24
But b=-a so LHS is (x-a)(x+a)(x-v)=(x^2-a^2)(x-v)
Multiplying the left hand side out we get:
From this we see that v=2 which implies 24=2*a^2
then a^2=12 but -a^2*x=kx