Find all zeroes of the polynomial (2x4-9x3 + 5x2 + 3x-1) if two of its

1.	Find all zeroes of the polynomial (2x4-9x3 + 5x2 + 3x-1) if two of its zeroes are (2 +伺and (2-5)
Answer» Since 2+√3 and 2-√3 are the roots Therefore (x-2-√3) and (x-2+√3) will be factors of the given polynomial. (2x⁴ -9x³ +5x²+3x-1) = (x-2-√3)(x-2+√3) .g(x) Now simply dividing (2x⁴ -9x³ +5x²+3x-1) by (x-2-√3) (x-2+√3) = (x-2)² - 3 = x²–4x+1 (2x⁴ -9x³ +5x²+3x-1) / (x²–4x+1) =( 2x²-x-1) Therefore g(x)= 2x²-x-1 =( x-1) (2x+1). Therefore other two roots are 1, -1/2 .

Find all zeroes of the polynomial (2x4-9x3 + 5x2 + 3x-1) if two of its zeroes are (2 +伺and (2-5)

Answer»

Since 2+√3 and 2-√3 are the roots

Therefore (x-2-√3) and (x-2+√3) will be factors of the given polynomial.

(2x⁴ -9x³ +5x²+3x-1) = (x-2-√3)(x-2+√3) .g(x)

Now simply dividing (2x⁴ -9x³ +5x²+3x-1) by

(x-2-√3) (x-2+√3) = (x-2)² - 3 = x²–4x+1

(2x⁴ -9x³ +5x²+3x-1) / (x²–4x+1)

=( 2x²-x-1)

Therefore g(x)= 2x²-x-1 =( x-1) (2x+1).

Therefore other two roots are 1, -1/2 .