Question
The straight line 2x + y –1= 0 meets the parabola y2 = 4x in
- Two real and different points
- Two imaginary points
- Two coincident points
- One real point and one point at infinity
Hint:
replace the value of y into the equation of parabola.
The correct answer is: Two real and different points
Two real and different points
2x+y-1=0
y = 1-2x
y2= 4x
(1-2x)2=4x
1+ 4x2-4x = 4x
4x2 -8x + 1=0
Here, D= 64- 16 = 48
D>0
Hence, there are 2 real and distinct roots
when D> 0, two real and distinct roots
when D=0, real and equal roots
when D<0 imaginary roots.
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