Math, asked by anjumghousia7786, 2 months ago

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

Answers

Answered by khinarampatle
25

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

Answered by user0888
73

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.

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