Question

How do you solve `x^4+2x^3=15x^2`?

Answer 1

`x=-5" or "x=0" or "x=3`

Explanation:

`"rearrange equation, equating to zero"`

`x^4+2x^3-15x^2=0`

`"take out a "color(blue)"common factor of "x^2`

`rArrx^2(x^2+2x-15)=0`

`"factorise the quadratic using the a-c method"`

`"the factors of - 15 which sum to + 2 are + 5 and - 3"`

`rArrx^2(x+5)(x-3)=0`

`"equate each factor to zero and solve for x"`

`x^2=0rArrx=0`

`x+5=0rArrx=-5`

`x-3=0rArrx=3`