At what points does the line 2x + y - 1 = 0 i | vedclass

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(A) Given the line $2x + y - 1 = 0$,we can express $y$ as $y = 1 - 2x$.Substitute this into the parabola equation $y^2 = 4x$:$(1 - 2x)^2 = 4x$$1 - 4x

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Two real and distinct points

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(A) Given the line $2x + y - 1 = 0$,we can express $y$ as $y = 1 - 2x$.Substitute this into the parabola equation $y^2 = 4x$:$(1 - 2x)^2 = 4x$$1 - 4x + 4x^2 = 4x$$4x^2 - 8x + 1 = 0$Now,calculate the discriminant $D = b^2 - 4ac$ for this quadratic equation:$D = (-8)^2 - 4(4)(1) = 64 - 16 = 48$.Since $D > 0$,the quadratic equation has two distinct real roots.Therefore,the line intersects the parabola at two real and distinct points.

At what points does the line $2x + y - 1 = 0$ intersect the parabola $y^2 = 4x$?

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