for what values of b is the line y=x+b a tangent to the curve y=2x^2-7x 4?

Question

Working out please!

Step by step..

Thank you!

Answer 1

It only intersects at one point

2x^2 - 7x + 4 = x+b

2x^2 - 7x + 4 - x - b = 0

2x^2 - 8x + (4-b) = 0

This quadratic equation must have only one solution.

So the discriminant is zero.

0 = B^2 - 4AC = (-8)^2 - 4(2)(4-b)

= 64 - 8(4-b)

= 64 - 32 + 8b

= 32 + 8b

-32 = 8b

b = -4