Question

Find all zeroes of the polynomial 8x^4+8x³-18x²-20x-5 . If it is given that two of its zeroes are √5/ 2 and - √5 /2 .

Answer 1

Step-by-step explanation:

(X+√5/2) (X-√5/2) = x^2-5/2 =2x^2-5

8x^4+8x^3-18x^2-20x-5÷2x^2-5 = 4x^2+4x+1

Then Factorise 4x^2+4x+1

4x^2+2x+2x+1

2x(2x+1)+1(2x+1)

(2x+1) (2x+1)

X= -1/2. X =-1/2

Therefore all zeroes are √5/2,-√5/2,-1/2,-1/2

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