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

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 = 0Let x1 and x2 be the roots of equation Sum of rootsSo, [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          ......AAnd  x1 × x2 = [tex]\frac{-6}{1}[/tex]Or,  x1 × x2 = - 6Now, (x1 - x2)² = (x1 + x2)²+ 4×x1×x2 Or,  (x1 - x2)² = (1)²+ 4×6Or,  (x1 - x2)² = 25So , 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