Examine whether the following equation is qua | vedclass

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(A) Given equation: $x^{3}-4x^{2}-x+1=(x-2)^{3}$.Expanding the right side using the identity $(a-b)^{3} = a^{3}-3a^{2}b+3ab^{2}-b^{3}$:$(x-2)^{3} = x^

Vedclass · Accepted Answer

Yes,it is a quadratic equation.

Vedclass · Answer

(A) Given equation: $x^{3}-4x^{2}-x+1=(x-2)^{3}$.Expanding the right side using the identity $(a-b)^{3} = a^{3}-3a^{2}b+3ab^{2}-b^{3}$:$(x-2)^{3} = x^{3}-3(x^{2})(2)+3(x)(2^{2})-(2)^{3} = x^{3}-6x^{2}+12x-8$.Now,substitute this back into the equation:$x^{3}-4x^{2}-x+1 = x^{3}-6x^{2}+12x-8$.Subtract $x^{3}$ from both sides:$-4x^{2}-x+1 = -6x^{2}+12x-8$.Rearrange all terms to one side:$(-4x^{2}+6x^{2}) + (-x-12x) + (1+8) = 0$.$2x^{2}-13x+9 = 0$.Since the equation is in the form $ax^{2}+bx+c=0$ where $a 
eq 0$,it is a quadratic equation.

Examine whether the following equation is quadratic or not: $x^{3}-4x^{2}-x+1=(x-2)^{3}$

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