Question

Hi, could anyone help me with this please?
The straight line l with equation y = 5 - 3x cuts the curve C, with equation y = 20x - 12x^2, at the points P and Q. Use algebra to find the exact coordinates of the points P and Q.
Any help would be really appreciated.

Answer 1

Answer:

Coordinates of P is (5/3,0) and Q is (1/4,17/4)

Step-by-step explanation:

You need to solve the simultaneous equation

y=5-3x -------> 1st equation

y=20x-12x^2 ---- >2nd eqation

equate them

5-3x = 20x-12x^2

take all the terms to one side

(12x^2)-(23x)+5=0

then factorize them

(3x-5)(4x-1)=0

therefore x=5/3 and x=1/4

then substitute x=5/3 and x=1/4 to the first equation to get the y coordinates

y=5-3(5/3)

y=0

and

y=5-3(1/4)

y=17/4 or 4.25

Hope its helpful to you.