A) \[\left( x-5y \right)\left( x-3y \right)\]
B) \[\left( x+5y \right)\left( x+3y \right)\]
C) \[\left( x-5y \right)\left( x+3y \right)\]
D) \[\left( x+5y \right)\left( x-3y \right)\]
Correct Answer: D
Solution :
(d): \[{{x}^{2}}+2xy-5{{y}^{2}}\] Considered it as a quadratic in x, Then roots= \[=\frac{-2y\pm \sqrt{4{{y}^{2}}-4\times 1\times (-15{{y}^{2}})}}{2}\] \[=\frac{-2y\pm \sqrt{64{{y}^{2}}}}{2}\] \[=\frac{-2y\pm 8y}{2}=-\,5y\,\,\text{or}\,\,3y\] \[\Rightarrow \left( x-3y \right)\left( x+5y \right).\]
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