A) \[(4{{x}^{2}}+8x-6),(4{{x}^{2}}-10x+2)\]
B) \[(2{{x}^{2}}+4x-3),(3{{x}^{2}}-10x-6)\]
C) \[(3{{x}^{2}}+4x-7),(2{{x}^{2}}-5x+3)\]
D) \[(3{{x}^{2}}+4x+7),(2{{x}^{2}}-5x-3)\]
Correct Answer: C
Solution :
Let the two expressions are \[X\] and\[Y\], then by hypothesis, \[X+Y=5{{x}^{2}}-x-4\] ? (i) and \[X-Y={{x}^{2}}+9x-10\] ... (ii) Adding and subtracting both equations, we get \[2X=6{{x}^{2}}+8x-14\] or \[X=3{{x}^{2}}+4x-7\] and \[2Y=4{{x}^{2}}-10x+6\] or \[Y=2{{x}^{2}}-5x+3\]
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