Question

Graph -x^2+x+6=0 and state the consecutive integers between which roots are located

Answer 1

Answer:

The roots of given quadratic equation lies from $\begin{bmatrix}-2 , 3 \end{bmatrix}$

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, $x1 + x2 = \frac{-b}{a}$  

And products of roots is x1 × x2 = $\frac{c}{a}$

So, $x1 + x2 = \frac{1}{1}$  

Or,   x1 + x2 = 1          ......A

And  x1 × x2 = $\frac{-6}{1}$

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 = $\sqrt{25}$ = 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 $\begin{bmatrix}-2 , 3 \end{bmatrix}$   Answer