Question

Find all the zeroes of the polynomial ^4 − 8^3 + 19^2 − 12 + 2,if two of its zeroes are 2+√2 and 2-√2

Answer 1

Answer:

the factors of 9 are 1, 3, and 9, and the factors of 49 are 1, 7, and 49.

Answer 2

Step-by-step explanation:

since two zeroes of the given polynomial are 2 + √2 and 2 - √2 , the polynomial should have two factors (x-2-√2) and (x-2+√2) that means it has quadratic factor (x-2-√2) X (x-2+√2)=(x-2)^2 -2= x2-4x+2 Now x4 − 8x3 + 19x2 − 12x + 2 = x4-4x3+2x2-4x3+16x2-8x +x2-4x+2 =x2( x2-4x+2) − 4x ( x2-4x+2)+ ( x2-4x+2) =( x2-4x+2)( x2-4x+1) Hence other quadratic factor should be= (x4 − 8x3 + 19x2 − 12x + 20)/ ( x^2-4x+2) =( x2-4x+1) Solve ( x2-4x+1)=0 => (x-2)2-3=0 hence other two zeroes are 2 + √3 and 2 - √3