which statement about ( f(x)=4x^{2}-36x + 81 ) is true?\n(a) the zeros are ( \frac{3}{4} ) and ( -27 )…

which statement about ( f(x)=4x^{2}-36x + 81 ) is true?\n(a) the zeros are ( \frac{3}{4} ) and ( -27 ) because ( f(x)=(4x - 3)(x - 27) ).\n(b) the zeros are ( -\frac{3}{2} ) and ( \frac{27}{2} ) because ( f(x)=(2x + 3)(2x + 27) ).\n(c) the zeros are ( pm\frac{9}{2} ) because ( f(x)=(2x - 9)(2x + 9) ).\n(d) the only zero is ( \frac{9}{2} ) because ( f(x)=(2x - 9)^{2} ).

which statement about ( f(x)=4x^{2}-36x + 81 ) is true?\n(a) the zeros are ( \frac{3}{4} ) and ( -27 ) because ( f(x)=(4x - 3)(x - 27) ).\n(b) the zeros are ( -\frac{3}{2} ) and ( \frac{27}{2} ) because ( f(x)=(2x + 3)(2x + 27) ).\n(c) the zeros are ( pm\frac{9}{2} ) because ( f(x)=(2x - 9)(2x + 9) ).\n(d) the only zero is ( \frac{9}{2} ) because ( f(x)=(2x - 9)^{2} ).

Answer

Explanation:

Step1: Expand the options

  • Expand ((4x - 3)(x - 27)=4x^{2}-108x - 3x+81=4x^{2}-111x + 81\neq4x^{2}-36x + 81)
  • Expand ((2x + 3)(2x + 27)=4x^{2}+54x+6x + 81=4x^{2}+60x + 81\neq4x^{2}-36x + 81)
  • Expand ((2x - 9)(2x + 9)=4x^{2}-81\neq4x^{2}-36x + 81)
  • Expand ((2x - 9)^{2}=(2x)^{2}-2\times2x\times9 + 9^{2}=4x^{2}-36x + 81)

Step2: Find the zero

Set (f(x)=(2x - 9)^{2}=0), then (2x-9 = 0), (x=\frac{9}{2})

Answer:

D. The only zero is (\frac{9}{2}) because (f(x)=(2x - 9)^{2})