Question

find all the roots of p (x) = x⁴-7x³-5x²+49x+46 if two roots are 5±√2​

Answer 1

Answer:

{- 2, - 1, 5 - √2, 5 + √2}

Step-by-step explanation:

If we plug in x = 1 or x = - 1 (the easiest numbers to calculate), we will see that (- 1) is zero for given polynomial, then

($x^{4}$ - 7x³ - 5x² + 49x + 46) ÷ (x + 1) = x³ - 8x² + 3x + 46

Let try x = - 2

(- 2)³ - 8(- 2)² + 3(- 2) + 46 = 0, thus (- 2) is another zero for given polynomial

( x³ - 8x² + 3x + 46) ÷ (x + 2) = x² - 10x + 23

Zeros for this one (x² - 10x + 23) is already given.

Thus, zeros for given function are {- 2, - 1, 5 - √2, 5 + √2}