Question

Find the roots of quadratic equation
by using completing the square method
i.e
2x² + x - 6=0.​

Answer 1

Step-by-step explanation:

6x² - x - 2 = 0

⇒ 6x² - 4x + 3x - 2 = 0

⇒ 2x(3x - 2) +1(3x - 2) = 0

⇒ (2x+1)(3x - 2) = 0

so either (3x - 2) = 0 or (2x+1) = 0

x = 2/3 or -1/2

Answer 2

$2x^2+x-6$

                      $=2(x^2+\dfrac{1}{2} x)-6$

                      $=2(x^2+\dfrac{1}{2} x+\dfrac{1}{16} )-\dfrac{1}{8} -6$

                      $=2(x+\dfrac{1}{4} )^2-\dfrac{49}{8}$

The two solutions come from $(x+\dfrac{1}{4} )^2=\dfrac{49}{16}$.

This is equivalent to $x+\dfrac{1}{4}=\pm\dfrac{7}{4}$.

So, solutions are  $x=2,\dfrac{3}{2}$.

More information

What is discriminant?

Let's graph the quadratic equation.

$y=2x^2+x-6$

     $=2(x^2+\dfrac{1}{2} x)-6$

     $=2(x^2+\dfrac{1}{2} x+\dfrac{1}{16} )-\dfrac{1}{8} -6$

     $=2(x+\dfrac{1}{4} )^2-\dfrac{49}{8}$

Here, the discriminant is $\dfrac{49}{16}$.

The graph is symmetric against $x=-\dfrac{1}{4}$ therefore two points are marked on

the x-axis. So, the graph has two real solutions. This is the main concept of discriminant.