Which of the following is not a quadratic equation?a)(x−2)2+1=2x−3b)x(x+1)+8=(x−2)(x−2)c)x(2x+3)=x2+1d)(x−2)3=x3−4

Hint: A quadratic equation is any equation that can be rearranged in standard form as ax2+bx+c=0 , where x represents an unknown, and a, b, and c represent known numbers, and a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no x2 term. The numbers a, b, and c are the coefficients of the equation and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term. Complete step-by-step answer: We will check every option for the non-quadratic equation. The equation which is not in the form of the standard 2-degree equation ax2+bx+c=0 where a≠0 are not a quadratic equation. Option a: Given, (x−2)2+1=2x−3. ⇒x2−4x+4+1=2x−3. ⇒x2−4x+5=2x−3. ⇒x2−6x+8=0. Therefore, option a is a quadratic equation. Option b: Given, x(x+1)+8=(x−2)(x−2) ⇒x2+x+8=x2−4x+4 ⇒5x+4=0 Here, the coefficient of x2 is zero. Therefore, the equation is a linear equation. Hence, Option b is not a quadratic equation. Option c: Given, x(2x+3)=x2+1 ⇒2x2+3x=x2+1 ⇒x2+3x−1=0 Therefore, option c is a quadratic equation. Option d: Given, (x−2)3=x3−4 ⇒x3+6x2−12x−8=x3−4 ⇒6x2−12x−4=0 Therefore, option d is a quadratic equation. Therefore, the correct option is option(b). Note: Don’t get confused that in option (b) , the LHS has a quadratic coefficient which is not equal to zero, because the RHS also has a second-degree term with the same quadratic coefficient. The second-degree term will cancel out and will leave a linear equation. Hence, it will not be a quadratic equation.