CHECK IF THE GIVEN EXPRESSION FORM A QUADRATIC EQUATION

Check If the Given Expression Form a Quadratic Equation :

The general form of any quadratic equation is

ax² + bx + c  =  0

Here a ≠ 0

If the expression can be expressed in the general form, we may say that the given expression is quadratic equation.

(i) (x + 1)² = 2 (x – 3)

Solution :

(x + 1)²  =  2 (x – 3) can be rewritten as

(a + b)²  =  a² + 2ab + b²

x²+ 2 x + 1  =  2 x – 6

x²+ 2 x – 2 x + 1 + 6  =  0

x² + 7  =  0

This exactly matches the general form of quadratic equation. So, the given equation is quadratic equation.

(ii) x² – 2 x  =  (-2) (3 – x)

Solution :

x² – 2 x  =  - 6 + 2 x

x² – 2 x – 2 x + 6  =  0

x² – 4 x + 6  =  0

This exactly matches the general form of quadratic equation.

(iii) (x - 2) (x + 1) = (x - 1) (x + 3)

Solution :

x² + 1x – 2x - 2  =  x² + 3x - 1x - 3

x² - 1x - 2  =  x² + 2x - 3

x² - x²- 1x - 2x - 2 + 3  =  0

 - 3x + 1  =  0

It does not match with the general form of quadratic equation. So the given equation is not a quadratic equation.

(iv) (x - 3) (2x + 1)  =  x (x + 5)

Solution :

2x² + 1x – 6x - 3  =  x² + 5x

2x² – 5x - 3  =  x² + 5x

2x²- x² - 5x – 5x - 3  =  0

x² - 10x - 3  =  0

This exactly matches the general form of quadratic equation. So the given equation is a quadratic equation.

(v) (2 x - 1) (x - 3)  =  (x + 5) (x - 1)

Solution :

2 x² - 6 x – x + 3  =  x² - 1 x - 5 x - 5

2 x² - 7 x + 3  =  x² - 6 x - 5

2 x²- x²- 7 x + 6 x + 3 + 5  =  0

x² - 1 x + 8  =  0

This exactly matches the general form of quadratic equation. So, the given equation is a quadratic equation.

(vi) x² + 3 x + 1 = (x - 2)²

Solution :

x² + 3 x + 1 = x² - 2 x (2) + 2²

x² + 3 x + 1 = x² - 4 x + 4

x²- x² + 3 x + 4 x + 1 - 4 = 0

7 x - 3 = 0

This does not match the general form of quadratic equation. So, the given equation is not a quadratic equation.

(vii) (x + 2)³ = 2 x (x² - 1)

Solution :

x³ +  3 (x²) (2) + 3 (x) (2)² + 2³  =  2 x³ - 2 x

x³ +  6 x² + 12 x + 8  =  2 x³ - 2 x

x³ - 2 x³ +  6 x² + 12 x + 2 x + 8   =  0

- x³ + 6 x² + 12 x + 2 x + 8  =  0

This does not exactly match the general form of quadratic equation. So the given equation is not a quadratic equation.

(vii) x³ - 4 x² - x + 1  =  (x - 2)³

Solution :

x³ - 4 x² - x + 1 = x³ -  3 (x²) (2) + 3 (x) (2)² - 2³

x³ - 4 x² - x + 1 = x³ -  6 x² + 12 x - 8

x³- x³ - 4 x² + 6 x² - x - 12 x + 1 + 9 = 0

2 x² - 13 x + 10 = 0

This exactly matches with the general form of quadratic equation. So the given equation is a quadratic equation.

After having gone through the stuff and examples,  we hope that the students would have understood, check if the given expression form a quadratic equation.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.