Obtain all other zeroes of the polynomial x^4+4x^3-2x^2-20x-15 if two of its zeroes are √5 and -√5
Answers
Answered by
27
here, given.. the two zeroes are (x-√5)and (x+√5)
so, multiplying those.. gives (x²-5)
dividing x⁴+4x³-2x²-20x-15 by (x²-5)
gives, quotient= x²+4x+3.... and remainder=0
so, factorising quotient...
x²+(3x+x)+3=0
x (x+3)+1(x+3)=0
so, x+3=0 or x+1=0
:; x=-3 or x=-1
Therefore, the zeroes of f(x) = √5, -√5, -3, -1
so, multiplying those.. gives (x²-5)
dividing x⁴+4x³-2x²-20x-15 by (x²-5)
gives, quotient= x²+4x+3.... and remainder=0
so, factorising quotient...
x²+(3x+x)+3=0
x (x+3)+1(x+3)=0
so, x+3=0 or x+1=0
:; x=-3 or x=-1
Therefore, the zeroes of f(x) = √5, -√5, -3, -1
Gokusparx:
Thank u
Similar questions