Consider the expression .

MATHEMATICS · Multi-part · CBSE · Mathematics · Polynomials · Polynomials

Problem

Consider the expression 12x4−48x2+3612x^{4}-48x^{2}+36. (i) Extract the greatest common factor (GCF) and write the simplified expression. (ii) Factor the resulting quadratic expression completely. (iii) Hence, obtain the complete factorisation of 12x4−48x2+3612x^{4}-48x^{2}+36. (iv) Using the factorised form, solve the equation 12x4−48x2+36=012x^{4}-48x^{2}+36=0, clearly listing all real roots.

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