Question

find all zeroes of polynomial (2x^4-9x^3+5x^2+3x-1)if two of its zeros are (2+‚àö3) and(2-‚àö3)

Answer 1

When U divide the p(x) by the roots,

p(x) = 2x⁴-9x³+5x²+3x-1

g(x) = x²-4x+1 (Because x = 2+√3 ⇒ (x-2-√3) and x = 2-√3 ⇒ (x-2+√3),

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

After Dividing p(x) / g(x)  ⇒ q(x) = 2x²-x-1

                                             r(x) = 0
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And zeroes are 2x²-x-1

= 2x²-x-1

= 2x²-2x+x-1

= 2x(x-1) +1(x-1)

= (2x+1)(x-1)

Then x = -1/2 and 1
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Hence all the zeroes are 2+√3, 2-√3, -1/2, 1
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