SOLUTION: a) show that the equation 0.25x squared - 0.7+ 1.5 =0 does not have any real roots. b) the line y=2x - 5 and the curve xsquared + xy = 2 intersects at the point A and B, show th

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Question 762677: a) show that the equation 0.25x squared - 0.7+ 1.5 =0 does not have any real roots.
b) the line y=2x - 5 and the curve xsquared + xy = 2 intersects at the point A and B, show that the equation to find the points A and B is givin by:
3xsquared - 5x - 2 = 0.
Hence find the coordinates of A and B.
Answer by malglu(63) (Show Source):
You can put this solution on YOUR website!
use the determinant b^2-4ac
which is
(-0.7)^2 - 4 x 0.25 x 1.5
this = -1.01
when the determinant is less then 0 then the roots are not real.
the points A and B obviously are on both the line and the curve. to find them we neeed to put 2x -5 in the equation of the curve whenever it has y
x^2 + (2x-5)x -2 =0
i have then -2 on each side so i can equal the equation to 0. the equation is now
x^2 + 2x^2 -5x -2=0
3x^2 -5x -2 =0
now find the roots of this equation
i used the formula to get x=2 and x= -1/3
put these values into any of the original equtions to get the y co-ordinates.
y=2x-5, so when x = 2 y = -1 and when x=-1/3 y=-17/3. these are the points A and B