Question

find the roots of the equation x^2-x=6​

Answer 1

Answer :

x = 3 , -2

Solution :

Method 1 : Middle term splitting :

Here ,

The given quadratic equation is ;

=> x² - x = 6

=> x² - x - 6 = 0

=> x² - 3x + 2x - 6 = 0

=> x(x - 3) + 2(x - 3) = 0

=> (x - 3)(x + 2) = 0

=> x = 3 , -2

Method 2 : By quadratic formula :

Here ,

The given quadratic equation is ;

=> x² - x = 6

=> x² - x - 6 = 0

Now ,

Comparing the above quadratic equation with the general quadratic equation ax² + bx + c = 0 , we have ;

a = 1

b = -1

c = -6

Now ,

The discriminant of the given quadratic equation will be given as ;

=> D = b² - 4ac

=> D = (-1)² - 4•1•(-6)

=> D = 1 + 24

=> D = 25

Now ,

The roots of the given quadratic equation will be given as ;

=> x = (-b ± √D)/2a

=> x = [ -(-1) ± √25 ] / 2•1

=> x = (1 ± 5)/2

=> x = (1 + 5)/2 , (1 - 5)/2

=> x = 6/2 , -4/2

=> x = 3 , -2

Hence ,

The roots of the given quadratic equation are x = 3 , -2 .

Answer 2

Answer:

Question

find the roots of the equation x^2-x=6

Answer

${x}^{2} - x = 6$

${x}^{2} - x - 6 = 0$

${x}^{2} - 3x - 2x - 6 = 0$

$x \: (x - 3) + 2(x - 3) = 0$

$(x - 3) \: + (x + 2) = 0$

$\huge \fbox {roots \: = 3 \: and \: -2}$