Thread: Simultaneous Linear and Quadratic Equations

Now I know the rules about this one, But I can't work out the second half of the sum,

1st half:
1. Find the value of such that the line with equation is a tangent to the parabola with equation




the determinant = 0 then there is only one intersection (tangent)

through DOPS




therefore

Now this is the part, I don't understand,

2. Find the possible values of c such that the line with equation twice intersects the parabola with equation

Any help would be much appreciated,

Thanks,

22upon7

Originally Posted by 22upon7

Now I know the rules about this one, But I can't work out the second half of the sum,

1st half:
1. Find the value of such that the line with equation is a tangent to the parabola with equation




the determinant = 0 then there is only one intersection (tangent)

through DOPS




therefore

Now this is the part, I don't understand,

2. Find the possible values of c such that the line with equation twice intersects the parabola with equation

Any help would be much appreciated,

Thanks,

22upon7

You require the discriminant to be greater than zero.

Thanks, so would that be proved like this:







Therefore

Originally Posted by 22upon7

Thanks, so would that be proved like this:







Therefore

The discriminant of is not .

Once you calculate correct discriminant you need to solve the following inequality for c:

discriminant > 0.