Find the roots of the equation x² - 5x + 6 = 0 using the quadratic formula.

A quadratic equation is an equation in the form of ax² - bx + c = 0 where a is a non-zero value.

Answer: Using the quadratic formula, the roots of the equation x² - 5x + 6 are 2 and 3.

Let's find the roots of the given quadratic equation.

Explanation:

x= [-b + √ b² - 4ac] / 2a   ---------(1)

or x= [-b - √ b² - 4ac] / 2a   --------(2)

On substituting the values of a = 1, b = - 5 and c = 6 in (1), we get

⇒ [-(-5) + √ {(-5)² - 4(1)(6)}] / 2 (1)

⇒ [5 + √ {25 - 24}] / 2

⇒ [5 + √1] / 2

⇒ 6 / 2

⇒ 3

On substituting the value a = 1, b = - 5 and c = 6 in (2), we get

⇒ [-(-5) - √ {(-5)² - 4(1)(6)}] / 2(1)

⇒ [5 -  √ {25 - 24}] / 2

⇒ [5 - √1] / 2

⇒ 4 / 2

⇒ 2

Thus. the roots of the equation x² - 5x + 6 are 2 and 3.