Math Methods Units 1&2

[Rose34]

Find the value(s) of a such that the line with equation y = x is tangent to the parabola with equation y = x^2 + ax+ 1.

[whys]

Find the value(s) of a such that the line with equation y = x is tangent to the parabola with equation y = x^2 + ax+ 1.

Tangent = intersecting at a point.
Let y=x equal y=x^2 + ax+ 1.
x=x^2 + ax+ 1.
Bring all x to one side.
x^2 + x(a - 1) +1=0.
Find the discriminant. Equate the discriminant to zero (this is when it will have one solution. this is what we want, as the question states 'tangent'). Thus find the value of a.

[Rose34]

Tangent = intersecting at a point.
Let y=x equal y=x^2 + ax+ 1.
x=x^2 + ax+ 1.
Bring all x to one side.
x^2 + x(a - 1) +1=0.
Find the discriminant. Equate the discriminant to zero (this is when it will have one solution. this is what we want, as the question states 'tangent'). Thus find the value of a.

Thank you so much