Math's: Quadratic Equations: Meaning and Standard Form, Standard Form of Quadratic Equations

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Quadratic Equations- Meaning

A polynomial of degree two is called a quadratic polynomial. When a quadratic polynomial is equated to zero, it is called a quadratic equation.

Example- .

1. Which of the following are quadratic equations?

(i)

(ii)

(iii)

(iv)

(v)

(vi)

Solution (i) can be written as . LHS is not a quadratic polynomial since the highest power is . Therefore, the equation is not a quadratic equation.

(ii) can be written as Since, the LHS is a quadratic polynomial, the equation is a quadratic equation.

(iii) is a quadratic equation as the LHS is a quadratic polynomial.

(iv) In , the LHS is not a polynomial as in the middle term the variable has a fractional power. So, the equation is not a quadratic equation.

(v) is a quadratic equation as the equation can be written as-

Now, LHS is a quadratic polynomial which makes the equation a quadratic equation.

Standard Form of Quadratic Equations

A quadratic equation of the form , where are constants and is a variable is called a quadratic equation in the standard form. Every quadratic equation can always be written in the standard form.

2. Which of the following quadratic equations are in standard form? Those which are not in standard form, express them in standard form.

(i)

(ii)

(iii)

(iv)

(v)

Sol- (i) is in standard form as it is in the form of .

(ii) is not in standard form. Its standard form is:

(iii) is not in standard form as it is in factorized form. Its standard form is

(iv) is not in standard form. Its standard form is

(v) is in the standard form as it is in the form of , .

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