Question

the roots of the quadratic equation in complete square method m2-3m+1=0​

Answer 1

Answer:

$\boxed{\sf m = \dfrac{3}{2}\pm\dfrac{\sqrt{5}}{2} }$

Step-by-step explanation:

We need to find the roots of a quadratic equation by completing the square Method . The quadratic equation is ,

$\sf\dashrightarrow m^2 - 3m + 1 = 0$

• Firstly we need to make the coefficient of m² as 1 , which is already present .

$\sf\dashrightarrow m^2 - 2\bigg(\dfrac{3m}{2}\bigg) + 1 = 0 \\\\\sf\dashrightarrow m^2 - 2\bigg(\dfrac{3m}{2}\bigg) +\bigg(\dfrac{3}{2}\bigg)^2 = \bigg(\dfrac{3}{2}\bigg)^2 - 1$

• Now the LHS is in the form of ( a - b)² form which equals to a² + b² - 2ab .

$\sf\dashrightarrow \bigg( m - \dfrac{3}{2}\bigg)^2 =\dfrac{9}{4}-1 \\\\\sf\dashrightarrow \bigg( m -\dfrac{3}{2}\bigg)^2 =\dfrac{ 9-4}{4} \\\\\sf\dashrightarrow \bigg( m - \dfrac{3}{2}\bigg)^2 =\dfrac{5}{4}\\\\\sf\dashrightarrow \bigg( m - \dfrac{3}{2}\bigg) =\pm \dfrac{\sqrt{5}}{2} \\\\\sf\dashrightarrow \boxed{\pink{\sf m = \dfrac{3}{2}\pm\dfrac{\sqrt{5}}{2} }}$