Question

What are quadratic equations?

Answer 1

Definition of a quadratic equation:

A quadratic equation is a polynomial of degree $2$ in one variable of the type $f\left(x\right)=a{x}^2+bx+c$,

here, $a\mathrm{and}b$ are coefficients and $c$ is any constant where the leading coefficient,$a\ne 0$.

Roots of the quadratic equation:

• The values of $x$ that satisfy the quadratic equation are called the roots of the quadratic equation.
• If $\alpha$ and $\beta$ are the roots of the quadratic equation $f\left(x\right)=a{x}^2+bx+c$ then it implies $f\left(\alpha \right)=0$ and$f\left(\beta \right)=0$. A quadratic equation of the form $a{x}^2+bx+c=0$ two distinct real or complex roots or two equal real or complex roots.
• The real roots of an equation $f\left(x\right)=0$ are the $x$ coordinates of the points where the curve intersect the$x-\mathrm{axis}$.

Thus, a quadratic equation is a polynomial of degree $2$ in one variable of the type $f\left(x\right)=a{x}^2+bx+c$.