Question

if two zeros of the polynomial f(x)=2x⁴+x³- 14x² + 5x + 6 are 2 and 1, find other zeros.​

Answer 1

Answer:

Since two zeroes are -2 and -1

then (X+2)(X+1) = x² +x+2x +2 = x²+3x +2 is a factor of the given polynomial. Now we divide the given polynomial by x²+3x +2

(2x⁴+x³-14x²-19x -6)/ (x²+3x +2)= 2x²-5x-3

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So 2x⁴+x³-14x²-19x -6= (x²+3x +2)(2x²-5x-3)

Now we factorise 2x²-5x-3

2x²-5x-3 = 0

2x²-6x + x-3= 0

2x (x -3)+1(x-3)=0

(2x+1)(x-3)=0

2x +1 = 0 or x-3 = 0

X=-1/2 or X= 3

Therefore,the zeroes of the given polynomial are -2,-1,-1/2 and 3