Find a quadratic function with zeros at #a+4# and #2a# where #a# is a constant. Write the function in standard form #f(x)=ax^2+bx+c#, and give the values of #a#, #b# and #c#. Assume the leading coefficient is 1?

1 Answer
Feb 20, 2018

#f(x) = x^2-(3a+4)x+(2a^2+8a)#

with coefficients #1#, #-(3a+4)# and #2a^2+8a#

Explanation:

A polynomial has a zero #x=alpha# if and only if it has a factor #(x-alpha)#

So given zeros #a+4# and #2a#, the required quadratic must have factors #(x-(a+4))# and #(x-2a)#

So we can write:

#f(x) = (x-(a+4))(x-2a)#

#color(white)(f(x)) = x^2-(3a+4)x+(2a^2+8a)#

So the three coefficients are #1#, #-(3a+4)# and #2a^2+8a#