##### Quadratic eq. and graphs - WAS...
###### The graph of the curve y = 2x2 - x -1 and a straight line PQ were drawn to solve the equation 2x2 - 5x+2 =0. What is the equation of the line PQ?

Correct Answer

Incorrect Answer

How to get the right answer:

Let the straight line be px+q

According to the question, the solution of the curve 2x2 - 5x+2 = 0 is when y = 2x2 - x - 1 = px+q

$2x^2 - x - 1 = px+q$

Rearrange this

$2x^2&space;-&space;x-px&space;-&space;1-q&space;=&space;0&space;\Rightarrow&space;2x^2&space;-&space;(1+p)x&space;-&space;(1+q)&space;=&space;0$

By comparing this expression to 2x2 - 5x+2 = 0, we can write

$1+p=5 \Rightarrow p=4$ and

$-(1+q)=2&space;\Rightarrow&space;q=-3$

Therefore the equation of line PQ is

$y=4x-3$