Question

find all zeroes of the polynomial ( 2x⁴- 9x³ + 5x² 3x -1 ) .... The two of its zeroes are (2+√3) and (2-√3)​

Answer 1

Answer:

Step-by-step explanation:

p(x)=2x^4 - 9x^3 + 5x^2 + 3x -1

x = ( 2+√3) , x = (2-√3)

(2+√3)(2-√3) = 0

= x^2 - 4x +1 = 0

On dividing p(x ) by the above polynomial using long division method we get the quotient as

2x^2 - x - 1

Now the zeroes of this quotient will also be the zeros of p(x)

On factorising the quotient by splitting the middle term , we get

2x^2 - x -1 =0

= 2x^2 - 2x + x -1 =0

= 2x(x - 1) + 1 (x - 1) = 0

= (2x + 1) (x - 1) = 0

Therefore

x = -1/2 and x = 1

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