What is Quadratic Equation in Standard Form

Here you will learn quadratic equation concepts and what is quadratic equation in standard form.

Let’s begin –

If p(x) is a quadratic polynomial, then p(x) = 0 is called a quadratic equation.

For example, $$x^2 + 2x – 8$$ = 0, $$x^2 – 5x + 6$$ = 0 are quadratic equations.

The general form of quadratic equation is $$ax^2 + bx + c$$ = 0. where a, b, c $$\in$$ R and a $$\ne$$ 0.

What is Quadratic Equation in Standard Form ?

The equation of the form $$ax^2 + bx + c$$ = 0, a $$\ne$$ 0 is known as standard equation.

For example, $$5x^2 + 3x + 6$$ = 0 is a quadratic equation in the standard form.

Rule to Determine Whether Equation is Quadratic or Not

1). Write down the given equation in the form f(x) = 0.

2). (a) If f(x) is a polynomial, then observe its degree.

(b) If f(x) is not a polynomial, then first make it poynomial and then observe its degree.

3). If degree of the polynomial is 2, then the given equation is quadratic.

Example : Which of the following are quadratic equation ?

(i) $$x^2 -6x – 4$$ = 0

(ii) x + 2 = 0

(iii) x + $$1\over x$$ = 1,  x $$\ne$$ 0

(iv) $$x^2$$ + $$1\over x$$ = 1,  x $$\ne$$ 0

Solution

(i) p(x) = $$x^2 -6x – 4$$ is polynomial with degree 2.

$$\therefore$$  $$x^2 -6x – 4$$ = 0 is a quadratic equation.

(ii) p(x) = x + 2 is polynomial with degree 1.

$$\therefore$$  x + 2 = 0 is not a quadratic equation.

(iii) x + $$1\over x$$ = 1 $$\implies$$ $$x^2 + 1\over x$$ = 1 $$\implies$$ $$x^2 +1$$ = x $$\implies$$ $$x^2 – x + 1$$ = 0

Since, here p(x) = $$x^2 – x + 1$$ is polynomial with degree 2.

$$\therefore$$  $$x^2 – x + 1$$ = 0 is a quadratic equation.

(iv)  $$x^2$$ + $$1\over x$$ = 1 $$\implies$$ $$x^3 + 1\over x$$ = 1 $$\implies$$ $$x^3 +1$$ = x $$\implies$$ $$x^3 – x + 1$$ = 0

Here, p(x) = $$x^3 – x + 1$$ is polynomial with degree 3.

$$\therefore$$  $$x^3 – x + 1$$ = 0 is not a quadratic equation.