Question

How do you find the roots for `4x^4-26x^3+50x^2-52x+84=0`?

Answer 1

The easiest way to find the roots (also known as zeroes and factors) of this equation would be to plug it in your graphing calculator, and find all 4 of them using 2ND`->`CALC`->`ZERO and find your roots (this video will show you exactly how to do that).

Now if your four zeroes are NOT all rational/real numbers, then you'd need to find one of your zeroes, and then use synthetic division till you got a quadratic, and then use factoring/the quadratic formula.

Here are videos for all the above ideas:

Synthetic Division

Factoring

Quadratic Formula

In your case, you have two real zeroes, and two unreal. Therefore, you'll need to condense this down to a quadratic using synthetic division, and then use quadratic formula.

The real zeroes are 3, 3.5, and the unreal zeroes are `+-isqrt(2)`. I'll leave the work for you to solve.

Hope that helped :)