Question

Find the roots of the quadratic equation 2x² + x − 6 = 0.

Answer 1

Given quadratic equation is 2x² + x − 6 = 0.

By comparing given quadratic equation with standard quadratic equation ax² + bx + c = 0, we get a = 2, b = 1 and c = −6.

And we know that the roots of the equation

Therefore, the roots of the given quadratic equation are

Hence, the roots of the quadratic equation 2x² + x − 6 = 0 are \(\frac{3}{2}\) and - 2.

Answer 2

Given quadratic equation - 2x² + x - 6 = 0

By comparing the above equations with ax² + bx + c          we get ,             a = 2  , b = 1 ,c = -6 

We know that , D = b² - 4ac 

D = 1 - 4 × 2 × (-6)  =  1 + 48    =  49   Since, D > 0  The equation have real but distinct roots .

Now,  By Quadratic Formula ,

 x = ( -b + √D ) / 2a 

 x = ( -1 + √49 ) / 2 × 2 

 x = ( -1 + 7 ) / 4

 x =  (-1+7) / 4       OR     x = (-1 -7)/4

 x =  6/4               ||           x = -8/4 

x =  3/2     or     x = -2  

Hence the roots of the quadratic equation are  3/2  or  -2  .