How do you find the number of possible positive real zeros and negative zeros then determine the rational zeros given #f(x)=x^4-5x^2+4#?

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Answer 1 · 2017-03-05T18:06:04

# (1) : f(x)" has two +ve zeroes, namely, "2 and 1;#

#(2) :" two "-ve "zeroes, "-2, and, -1:#

#(3) :" four rational zeroes, "+-2, +-1#.

Let #x^2=y# in #f(x)=x^4-5x^2+4=y^2-5y+4.#

#:. f(x)=0 rArr y^2-5y+4=0.#

#:. ul(y^2-4y)-ul(y+4)=0.#

#:. y(y-4)-1(y-4)=0.#

#:. (y-4)(y-1)=0.#

#:. (x^2-4)(x^2-1)=0, ...........[because, y=x^2]#

#:. (x+2)(x-2)(x+1)(x-1)=0.#

#:. x=-2, 2, -1, and, 1.#

Thus, # (1) : f(x)" has two +ve zeroes, namely, "2 and 1;#

#(2) :" two "-ve "zeroes, "-2, and, -1:#

#(3) :" four rational zeroes, "+-2, +-1#.

Enjoy Maths.!