Slove, writing any non-real solution in the form a+bi:x^4+10x^2=6x^3. Can you show details on how to answer please thank you for your help.

Question

Slove, writing any non-real solution  in the form a+bi:x^4+10x^2=6x^3. Can you show details on how to answer please thank you for your help.

campbell_st · Answer

rewrite your equation 

$$x^4 - 6x^3 + 10x^2 = 0$$

then factor 

$$x^2(x^2 -6x + 10) = 0$$

so the non-real solutions occur in the quadratic factor.

you need to solve the quadratic using the general quadratic formula and you'll find that the solutions will be in the form of 

x =a + bi

hope it helps

anonymous · Answer

I have an answer key that shows the answer is 0,3+i,3-i. Can you show me how they got this answer please, thanks

campbell_st · Answer

well zero is correct and comes from the factor x^2

so looking at the quadratic you need

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

where a = 1, b = -6 and c = 10

substitute and evaluate then you'll see if you get the required answers...