Explanation :

There are two methods to solve this question.

Method 1.

By Factoring Method:

∵ x² - 2x - 3 = 0

⇒ x(x - 3) + 1(x - 3) = 0

⇒ (x - 3)(x + 1) = 0

⇒ x = -1 or 3

Method 2.

By Quadratic Formula:

∵ x² - 2x - 3 = 0

As we know that,

x = $\dfrac{-b \pm \sqrt{\text{D}}}{2a}$

Where, D = b² - 4ac

Then, D = (-2)² - 4 x 1 x (-3)

⇒ D = 4 + 12 = 16

∴ x = $ \dfrac{-(-2) \pm \sqrt{16}}{2}$

⇒ x = $ \dfrac{-(-2) \pm 4}{2}$

⇒ x = $\dfrac{2 \pm 4}{2}$

⇒ x = $\dfrac{-2}{2}$ or $\dfrac{6}{2}$

⇒ x = -1 or 3

Explanation :

There are two methods to solve this question.

Method 1:

By Factoring Method:

∵ p² + 13p + 40 = 0

⇒ p² + 8p + 5p + 40 = 0

⇒ p(p + 8) + 5(p + 8) = 0

⇒ (p + 8)(p + 5) = 0

⇒ p = -8 or -5

Method 2:

By Quadratic Formula:

∵ p² + 13p + 40 = 0

As we know that,

x = $\dfrac{-b \pm \sqrt{\text{D}}}{2a}$

Where, D = b² - 4ac

Then, D = (-13)² - 4 x 1 x 40

⇒ D = 169 - 160 = 9

∴ p = $ \dfrac{-13 \pm \sqrt{9}}{2}$

⇒ p = $ \dfrac{-13 \pm 3}{2}$

⇒ p = $\dfrac{-16}{2}$ or $\dfrac{-10}{2}$

⇒ p = -8 or -5

Explanation :

There are two methods to solve this question.

Method 1:

By Factoring Method:

∵ x² - 3x + 2 = 0

⇒ x² - 2x - x + 2 = 0

⇒ x(x - 2) - 1(x - 2) = 0

⇒ (x - 2)(x - 1) = 0

⇒ x = 1 or 2

Method 2:

By Quadratic Formula:

∵ x² - 3x + 2 = 0

As we know that,

x = $\dfrac{-b \pm \sqrt{\text{D}}}{2a}$

Where, D = b² - 4ac

Then, D = (-3)² - 4 x 1 x 2

⇒ D = 9 - 8 = 1

∴ x = $ \dfrac{-(-3) \pm \sqrt{1}}{2}$

⇒ x = $ \dfrac{3 \pm 1}{2}$

⇒ x = $\dfrac{2}{2}$ or $\dfrac{4}{2}$

⇒ x = 1 or 2

Explanation :

There are two methods to solve this question.

Method 1:

By Factoring Method:

∵ x² + 3x - 10 = 0

⇒ x² + 5x - 2x + 10 = 0

⇒ x(x + 5) - 2(x + 5) = 0

⇒ (x + 5)(x - 2) = 0

⇒ x = -5 or 2

Method 2:

By Quadratic Formula:

∵ x² + 3x - 10 = 0

As we know that,

x = $\dfrac{-b \pm \sqrt{\text{D}}}{2a}$

Where, D = b² - 4ac

Then, D = (3)² - 4 x 1 x (-10)

⇒ D = 9 + 40 = 49

∴ x = $ \dfrac{-3 \pm \sqrt{49}}{2}$

⇒ x = $ \dfrac{-3 \pm 7}{2}$

⇒ x = $\dfrac{-10}{2}$ or $\dfrac{4}{2}$

⇒ x = -5 or 2

Explanation :

∵ x² - 7x = 0

⇒ x(x - 7) = 0

⇒ x = 0 or 7