What-is-the-condition-for-a-given-line-to-1-intersect-a-curve-2-be-a-tangent-to-a-curve-3-not-to-intersect-a-curve-

Question Number 116301 by harckinwunmy last updated on 02/Oct/20

What is the condition for a

given line to

1) intersect a curve

2) be a tangent to a curve

3) not to intersect a curve

Answered by Rio Michael last updated on 02/Oct/20

(1) b^{2} - 4 a c > 0

(2) b^{2} - 4 a c = 0

(3) b^{2} - 4 a c < 0

Answered by mr W last updated on 02/Oct/20

s a y t h e l i n e i s y = a x + b

t h e c u r v e i s y = f (x)

(1)

i f f (x) - a x - b = 0 h a s a t l e a s t o n e

r e a l r o o t, s a y t h e r o o t s a r e r_{i}, a n d

f^{'} (r_{i}) \neq a

(2)

a s (1) b u t f^{'} (r_{i}) = a

(3)

i f g (x) - a x - b = 0 h a s n o r e a l r o o t .

Facebook Tweet Pin