Answer:
Given, polynomial is \[{{x}^{4}}+5{{x}^{3}}+4{{x}^{2}}-10x-12\]. Since two zeroes are \[-2\] and \[-3\] \[\therefore (x+2)(x+3)={{x}^{2}}+3x+2x+6\] Dividing the polynomial with\[{{x}^{2}}+5x+6\], \[\therefore \,\,{{x}^{4}}+5{{x}^{3}}+4{{x}^{2}}-10x-12\] \[=({{x}^{2}}+5x+6)({{x}^{2}}-2)\] \[=(x+2)(x+3)(x-\sqrt{2})(x+\sqrt{2})\] Other zeroes: \[x-\sqrt{2}=0\] or \[x+\sqrt{2}=0\] \[x=\sqrt{2}\] or \[x=-\sqrt{2}\] The zeros of the polynomial are \[-2,-3,\sqrt{2}\] and \[-\sqrt{2}\]
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