# Application of Factor Theorem

We will discuss here about the application of Factor Theorem.

1. Find the roots of the equation 2x$$^{2}$$ - 7x + 6 = 0. Hence factorize 2x$$^{2}$$ - 7x + 6.

Solution:

Here, the equation is 2x$$^{2}$$ - 7x + 6 = 0

⟹ 2x$$^{2}$$ - 4x - 3x + 6 = 0

⟹ 2x(x - 2) - 3(x - 2) = 0

⟹ (x - 2)(2x - 3) = 0

⟹ x - 2 = 0 or 2x - 3 = 0

⟹ x = 2 or x = $$\frac{3}{2}$$

Therefore, 2x$$^{2}$$ - 7x + 6 = 2(x - 2)(x - $$\frac{3}{2}$$) = (x - 2)(2x - 3)

2. Find the quadratic equation whose roots are 1 + √3 and 1 - √3.

Solution:

We know that the quadratic equation whose roots are α and β, is

(x – α)(x – β) = 0

Therefore, the required equation is {x - (1 + √3)}{x - (1 - √3)} = 0

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

⟹ x$$^{2}$$ - 2x + (1 - 3) = 0

⟹ x$$^{2}$$ - 2x – 2 = 0.

3. Find the cubic equation whose roots are 2, √3 and -√3.

Solution:

We know that the quadratic equation whose roots are α, β and γ, is

(x – α)(x – β)(x - γ) = 0

Therefore, the required equation is (x – 2)(x - √3){x – (-√3)} = 0

⟹ (x - 2)(x - √3)(x + √3) = 0

⟹ (x - 2)(x$$^{2}$$ - 3) = 0

⟹ x$$^{3}$$ – 2x$$^{2}$$ - 3x + 6 = 0.

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

⟹ x$$^{2}$$ - 2x + (1 - 3) = 0

⟹ x$$^{2}$$ - 2x - 2 = 0.

4. Factorize x$$^{2}$$ -3x - 9

Solution:

The corresponding equation is x$$^{2}$$ - 3x - 9= 0

Now we apply the quadratic formula

x = $$\frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$$

= $$\frac{-(-3) \pm \sqrt{(-3)^{2} - 4 \cdot 1 \cdot (-9)}}{2 \cdot 1}$$

= $$\frac{3 \pm \sqrt{9 + 36}}{2}$$

= $$\frac{3 \pm \sqrt{45}}{2}$$

= $$\frac{3 \pm 3\sqrt{5}}{2}$$

Therefore, x$$^{2}$$ - 3x - 9 = (x - $$\frac{3 + 3\sqrt{5}}{2}$$)(x - $$\frac{3 - 3\sqrt{5}}{2}$$)

● Factorization

From Application of Factor Theorem to HOME

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

Apr 20, 24 05:39 PM

There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

2. ### What are Parallel Lines in Geometry? | Two Parallel Lines | Examples

Apr 20, 24 05:29 PM

In parallel lines when two lines do not intersect each other at any point even if they are extended to infinity. What are parallel lines in geometry? Two lines which do not intersect each other

3. ### Perpendicular Lines | What are Perpendicular Lines in Geometry?|Symbol

Apr 19, 24 04:01 PM

In perpendicular lines when two intersecting lines a and b are said to be perpendicular to each other if one of the angles formed by them is a right angle. In other words, Set Square Set Square If two…

4. ### Fundamental Geometrical Concepts | Point | Line | Properties of Lines

Apr 19, 24 01:50 PM

The fundamental geometrical concepts depend on three basic concepts — point, line and plane. The terms cannot be precisely defined. However, the meanings of these terms are explained through examples.