Question

quadratic equation...plzzz solve and explain

Answer 1

Given Equation is x^2 - 5x + 6 = 0

x^2 - 3x - 2x + 6 = 0

x(x - 3) - 2(x - 3) = 0

(x - 2)(x - 3) = 0

x = 2 (or) 3.


Hope this helps!

Answer 2

Hey there!

Solving it by applying quadratic formula for equation "x^2 - 5x + 6 = 0"

For a required quadratic equation of $\bf{ax^2 + bx + c = 0}$ the solutions for which can be represented by the quadratic formula of :

$\boxed{\bf{x_{1, \: 2} = \dfrac{- b +- \sqrt{b^2 - 4ac}}{2a}}}$

Here, a = 1,  b = - 5,  c = 6.

Solving for positive and negative values respectively:

$\bf{x_{1} = \dfrac{- (- 5) - \sqrt{(- 5)^2 - 4(1)(6)}}{2(1)}}$

$\bf{x_{1} = \dfrac{5 - \sqrt{25 - 24}}{2 \times 1}}$

$\bf{x_{1} = \dfrac{5 - 1}{2 \times 1}}$

$\bf{x_{1} = \dfrac{4}{2}}$

$\bf{\therefore \quad x_{1} = 2}$

For the second solution in Positive form of equation:

$\bf{x_{2} = \dfrac{- (- 5) + \sqrt{(- 5)^2 - 4(1)(6)}}{2(1)}}$

$\bf{x_{2} = \dfrac{5 + \sqrt{25 - 24}}{2 \times 1}}$

$\bf{x_{2} = \dfrac{5 + 1}{2 \times 1}}$

$\bf{x_{2} = \dfrac{6}{2}}$

$\bf{\therefore \quad x_{2} = 3}$

Therefore the final solutions for this quadratic equations are:

$\boxed{\underline{\bf{x_{1} = 2}}}$

$\boxed{\underline{\bf{x_{2} = 3}}}$

Hope this helps you and solves the doubts for getting the equation solved by quadratic method!