A-line-has-equation-y-2x-7-and-a-curve-has-equation-y-x-2-4x-c-where-c-is-a-constant-Find-the-set-of-possible-values-of-c-for-which-the-line-does-not-intersect-the-curve-

Question Number 25199 by tawa tawa last updated on 06/Dec/17

A line has equation y = 2 x - 7 and a curve has equation y = x^{2} - 4 x + c,

where c is a constant . Find the set of possible values of c for which the line

does not intersect the curve .

Commented by tawa tawa last updated on 06/Dec/17

options

(a) c < 2 (b) c > 2 (c) c = 2 (d) c > 1 / 0.5

Answered by Rasheed.Sindhi last updated on 06/Dec/17

y = 2 x - 7

y = x^{2} - 4 x + c

Solving above two simultaneously

x^{2} - 4 x + c = 2 x - 7

x^{2} - 6 x + c + 7 = 0

x = \frac{6 \pm \sqrt{36 - 4 c - 28}}{2}

x = \frac{6 \pm 2 \sqrt{2 - c}}{2} = 3 \pm \sqrt{2 - c}

x \in R \Rightarrow c ⩽ 2

For x = 3 \pm \sqrt{2 - c} where c ⩽ 2 the curve and the

line intersect with eachother .

So for c > 2, the line and curve will not

intersect .

Option (b) is correct .

Commented by tawa tawa last updated on 06/Dec/17

I really appreciate sir . God bless you sir .