Question

2z-3 is a factor of 2z^3 -z^2 +az -3
find a and all zeroes of the cubic. 2z-3 is a factor of 2z^3 -z^2 +az -3
find a and all zeroes of the cubic. @Mathematics

Answer 1

if 2z - 3 is a factor then f(3/2) = 0

2(3/2)^3 - (3/2)^2 + 3/2 a - 3 = 0

2 * 27/8 - 9/4 + 3a / 2 - 3 = 0
54 - 18 + 12a - 24 = 0
a = -54 + 18 + 24 / 12
a = -1

Answer 2

Use synthetic division. Put 3/2 on the shelf. 3/2(a+3) must =3. So a must be -1. FEMA ing factor is therefore 2z^2+2z+2. Use the quadratic formula to find that the remaining zeros are (-1+|-sqrt6)/2

Answer 3

factorising
(2z-3)(z^2 + z + 1) = 0

z = 3/2

z = -1 +- sqrt(1 - 4 *1*1) / 2

= [ -1 + sqrt3 i ] / 2 or [ -1 - sqrt3 i] / 2

Answer 4

what does that sqrt mean?

Answer 5

ohh square root??

Answer 6

yes

Answer 7

yea

Answer 8

ha thank you so much!!

Answer 9

if ound the z^2 + z + 1 by long division - i find i get into trouble with synthetic division

Answer 10

ok you can further simplify the complex roots

to -(1/2) +(1/2)i sqrt3 , -(1/2) - (1/2)i sqrt3

Answer 11

the sqrt refers to the 3 only

Answer 12

yapp!! :)