Quadratic Formula

PLEASE SHOW ALL WORK RELEVANT TO EACH ANSWER.
ANSWERS WITHOUT JUSTIFICATION WILL NOT RECEIVE CREDIT.
Please provide your justifications in paragraph form using full sentences.
Each problem is worth 10 points.

Please do not attempt to justify your answers by “plugging in” numbers . Use
variables and algebraic reasoning .

1) a) Use the quadratic formula to demonstrate algebraically that the
roots of ax ^2 + bx + c = 0 are the same as the roots of
kax^2 + kbx + kc = 0.

b) Give a particular example of this phenomenon.

c) Explain what this means in terms of solving equations of the form
kax^2 + kbx + kc =0 .

2) By the quadratic formula , the roots of a quadratic equation of the form
ax^2 + bx + c = 0 are given by


Demonstrate algebraically that
and that

Explain your reasoning in paragraph form.