Answer :

Answer:

The roots of given quadratic equation lies from [tex]\begin{bmatrix}-2 , 3 \end{bmatrix}[/tex]

Step-by-step explanation:

Given as :

The quadratic equation is x² - x -6 = 0

The quadratic equation is in form of ax² + bx +c = 0

Let x1 and x2 be the roots of equation

Sum of roots

So, [tex]x1 + x2 = \frac{-b}{a}[/tex]  

And products of roots is x1 × x2 = [tex]\frac{c}{a}[/tex]

So, [tex]x1 + x2 = \frac{1}{1}[/tex]  

Or,   x1 + x2 = 1          ......A

And  x1 × x2 = [tex]\frac{-6}{1}[/tex]

Or,  x1 × x2 = - 6

Now, (x1 - x2)² = (x1 + x2)²+ 4×x1×x2

Or,  (x1 - x2)² = (1)²+ 4×6

Or,  (x1 - x2)² = 25

So , x1 - x2 = [tex]\sqrt{25}[/tex] = 5          ......B

Now solve eq A and eq B

Or, (x1 + x2) + (x1 - x2) = 1 +5

Or, 2 x1 = 6

∴   x1 = 3     And     x2 = - 2

Hence The roots of given quadratic equation lies from [tex]\begin{bmatrix}-2 , 3 \end{bmatrix}[/tex]   Answer

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