Show that the roots of x 2 + b x + a c = 0 are a times the roots of the quadratic a x 2 + b x + c = 0 by using transformation of the function f ( x ) = a x 2 + b x + cLet f ( x ) = a x 2 + b x + c and g ( x ) = x 2 + b x + a cThe graph of y = g ( a x ) results from shifting the graph of y = g ( x ) horizontally b a factor of 1 / aDoes that mean g ( a x ) = f ( x )?

Question

Show that the roots of       x    2    +  b  x  +  a  c  =  0 are a times the roots of the quadratic   a      x    2    +  b  x  +  c  =  0  by using transformation of the function   f  (  x  )  =  a      x    2    +  b  x  +  cLet   f  (  x  )  =  a      x    2    +  b  x  +  c and   g  (  x  )  =      x    2    +  b  x  +  a  cThe graph of   y  =  g  (  a  x  ) results from shifting the graph of   y  =  g  (  x  ) horizontally b a factor of   1      /    aDoes that mean   g  (  a  x  )  =  f  (  x  )?

artirw9f · Accepted Answer

You have  a  f  (  x  )  =      a    2        x    2    +  a  b  x  +  a  c  =  (  a  x      )    2    +  b  (  a  x  )  +  a  c  =  g  (  a  x  )indeed. So,   f  (  x  )  =  0    ⟺    g  (  a  x  )  =  0 (assuming that   a  ≠  0).

Show that the roots of x^2+bx+ac=0 are a times the roots of the quadratic ax^2+bx+c=0 by using transformation of the function f(x)=ax^2+bx+c.

Answered question

Answer & Explanation

New Questions in Algebra I