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c1 question

Given thatf(x) = 2x^2 + 8x + 3
(a) find the value of the discriminant of f(x).
(b) Express f(x) in the form p(x + q)2 + r where p, q and r are integers to be found.

The line y = 4x + c, where c is a constant, is a tangent to the curve with equation y = f(x).
(c) Calculate the value of c.

i know how to do a and b, but dont understand c. Could someone explain the question.
Reply 1
Avatar for TeeEm
TeeEm
19
Original post by blankboi
Given thatf(x) = 2x^2 + 8x + 3
(a) find the value of the discriminant of f(x).
(b) Express f(x) in the form p(x + q)2 + r where p, q and r are integers to be found.

The line y = 4x + c, where c is a constant, is a tangent to the curve with equation y = f(x).
(c) Calculate the value of c.

i know how to do a and b, but dont understand c. Could someone explain the question.


equate the equation of the curve and the line as if you were looking for intersections.
move to one side as a quadratic in x
then think about the discriminant.
Reply 2
Avatar for blankboi
blankboi
OP
1
Original post by TeeEm
equate the equation of the curve and the line as if you were looking for intersections.
move to one side as a quadratic in x
then think about the discriminant.


hm i got 2x^2+4x+3 = c but don't know what to do next. Not sure what to do with the discriminant
Reply 3
Avatar for TeeEm
TeeEm
19
Original post by blankboi
hm i got 2x^2+4x+3 = c but don't know what to do next. Not sure what to do with the discriminant


2x2+4x+3 - c = 0
2x2+4x+ (3 - c) = 0

if tangent this discriminant should produce repeated roots
Reply 4
Avatar for Kenny56
Kenny56
5
Can anyone explain what this has to do with the discriminant
Reply 5
Avatar for davros
davros
16
Original post by Kenny56
Can anyone explain what this has to do with the discriminant


You really shouldn't resurrect 6 year old threads, but this is a standard technique - if a line touches a quadratic curve then solving the resultant quadratic equation should only produce a single (repeated) root which means that the discriminant = 0.

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