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Standard XII

Mathematics

Rectangular Cartesian Coordinate System

If abscissae ...

Question

If abscissae and ordinates of the points $A (x_{1}, y_{1})$ and $B (x_{2}, y_{2})$ are the roots of the quadratic equation $x^{2} - x - 1 = 0$ and $y^{2} - 2 y = 0$ respectively, then the distance $A B$ (in units) is

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Solution

The correct option is C $3$
Given : $x^{2} - x - 1 = 0 \Rightarrow x_{1} + x_{2} = 1, x_{1} x_{2} = - 1$
and $y^{2} - 2 y = 0 \Rightarrow y_{1} + y_{2} = 2, y_{1} y_{2} = 0$
$∴ A B = \sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}$
$= \sqrt{(x_{1} + x_{2})^{2} - 4 x_{1} x_{2} + (y_{1} + y_{2})^{2} - 4 y_{1} y_{2}}$
$= \sqrt{1 + 4 + 4 - 0} = 3$ units

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If abscissae and ordinates of the points A(x1,y1) and B(x2,y2) are the roots of the quadratic equation x2−x−1=0 and y2−2y=0 respectively, then the distance AB(in units) is

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