Question

Find which of the following equations are quadratic

(F) $(x-1{)}^2+(x+2{)}^2+3(x+1)=0$

Answer 1

Step: Finding whether the given equation is quadratic or not

The standard form of a quadratic equation is $a{x}^2+bx+c=0$, where a,b and c are all real numbers and $a\ne 0$.

$(a-b{)}^2=a^2+b^2-2ab$
$(a+b{)}^2=a^2+b^2+2ab$

Applying these identities and simplifying, the given equation becomes $2x^2+5x+8=0$

The given equation is of the form $a{x}^2+bx+c=0$

$\therefore$ Given equation is a quadratic equation.