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Which of the following option has the linear factors of 2x^2-xy-y^2+3y-2 ?

Option: 1

x+y-1\;\;and \;\;x+2y-2


Option: 2

x-y+1\;\;and\;\;2x+y-2


Option: 3

x-y+1\;\;and\;\;2x-y-2


Option: 4

x-y+1\;\;and\;\;x+y-2


Answers (1)

best_answer

Quadratic Equation in two Variables

\\\mathrm{Write\:in\:the\:standard\:form}\:ax^2+bx+c=0\\2x^2-yx-y^2+3y-2=0\\\\\mathrm{For\:}\quad a=2,\:b=-y,\:c=-y^2+3y-2:\\\\\quad x=\frac{-\left(-y\right)\pm \sqrt{\left(-y\right)^2-4\cdot \:2\left(-y^2+3y-2\right)}}{2\cdot \:2}\\\text{Taking '+' sign:}\,\,x=\frac{-\left(-y\right)+\sqrt{\left(-y\right)^2-4\cdot \:2\left(-y^2+3y-2\right)}}{2\cdot \:2}=\quad y-1

\text{Taking '-' sign:}\,\,x=\frac{-\left(-y\right)-\sqrt{\left(-y\right)^2-4\cdot \:2\left(-y^2+3y-2\right)}}{2\cdot \:2}=\frac{-y+2}{2}

So, x=y-1,\:x=\frac{-y+2}{2}

Correct option (2)

Posted by

Rishabh

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