Question

Find the roots of the quadratic equation:

`2x^(2) - x - 10 = 0`

Answer 1

2x^2 - x = 10

=> 2x^2 - x - 10 = 0

=> 2x^2 - (5 - 4)x - 10 = 0

=> 2x^2 - 5x + 4x - 10 = 0

=> x(2x - 5) + 2(2x - 5) = 0

=> (2x - 5)(x + 2) = 0

Either, Or,

2x - 5 = 0 x + 2 = 0

=> 2x = 5 => x = - 2

=> x = 5/2

Answer 2

`x1 = (5)/(2) \: \: and \: x2 = - 2`

Explanation:

So, our equation is:

2x² - x - 10 = 0

The numbers before x are a, b, and c

We must first find the discriminant which is equal to b² - 4*a*c

D = b² - 4 * a * c

Be careful here, b is -1 because we have minus before x and c is -10

D = (-1)² - 4*2*-10

D = 1 + 80

D = 81

Now we need to find the roots of the equation, since D is greater than 0, the roots are equal to (-b ± sqrt(D)) / 2*a

`x1 = ( -( - 1) + √(81) )/(2 * 2) = (1 + 9)/(4) = (10)/(4) = (5)/(2)`

and for x2 we will put minus:

`x2 = ( - ( - 1) - √(81) )/(2 * 2) = (1 - 9)/(4) = ( - 8)/(4) = -2`