Find the zeros of f ( x ) = x 2 + 4 x + 3 x 2 + 5 x + 6 a) {-1}, b) {-1,-3}, c){1,-3}, d) {1,3}

Question

Find the zeros of   f  (  x  )  =                    x        2            +      4      x      +      3                      x        2            +      5      x      +      6      a) {-1}, b) {-1,-3}, c){1,-3}, d) {1,3}

Erika Brady · Accepted Answer

Step 1  f  (  x  )  =                    x        2            +      4      x      +      3                      x        2            +      5      x      +      6        ⇒  f  (  x  )  =                    x        2            +      x      +      3      x      +      3                      x        2            +      2      x      +      3      x      +      6        ⇒  f  (  x  )  =            x      (      x      +      1      )      +      3      (      x      +      1      )              x      (      x      +      2      )      +      3      (      x      +      2      )        ⇒  f  (  x  )  =            (      x      +      1      )      (      x      +                        ⧸                            3            )              (      x      +      2      )      (      x      +                        ⧸                            3            )        ⇒  f  (  x  )  =            x      +      1              x      +      2      Step 2Zero&#039;s   ⇒  f  (  x  )  =  0  ⇒            x      +      1              x      +      2        =  0  ⇒  x  +  1  =  0  ⇒  x  =  −  1Zero&#039;s are {-1}

Find the zeros of f(x)=(x^2+4x+3)/(x^2+5x+6)

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