Question

X^2+X+7 can anyone say the answer

Answer 1

The roots of the equation x²+x+7 are $\alpha =\frac{-1+3i\sqrt{3 } }{2}$   and $\beta =\frac{-1-3i\sqrt{3 } }{2}$  

Explanation:

Given:

x²+x+7

To find:

The roots of the equation

Formula:

$\alpha =\frac{-b+\sqrt{b^{2}-4ac } }{2a}$

$\beta =\frac{-b-\sqrt{b^{2}-4ac} }{2a}$

Solution:

==> The equation is x²+x+7

==> a = coefficient of x²

==> b = coefficient of x

==> c = constant

==> a = 1

==> b = 1

==> c = 7

==> Apply the values in the formula

==> $\alpha =\frac{-b+\sqrt{b^{2}-4ac } }{2a}$

==>  $\alpha =\frac{-1+\sqrt{1^{2}-4(1)(7) } }{2(1)}$

==> $\alpha =\frac{-1+\sqrt{1-4(7) } }{2}$

==> $\alpha =\frac{-1+\sqrt{1-28 } }{2}$

==> $\alpha =\frac{-1+\sqrt{-27 } }{2}$

==> we know that, i²=-1

==> $\alpha =\frac{-1+\sqrt{-1\times27 } }{2}$

==> $\alpha =\frac{-1+\sqrt{i^{2} \times3\times3\times3 } }{2}$

==> $\alpha =\frac{-1+3i\sqrt{3 } }{2}$  

==> $\beta =\frac{-b-\sqrt{b^{2}-4ac } }{2a}$

==>  $\beta =\frac{-1-\sqrt{1^{2}-4(1)(7) } }{2(1)}$

==> $\beta =\frac{-1-\sqrt{1-4(7) } }{2}$

==> $\beta =\frac{-1-\sqrt{1-28 } }{2}$

==> $\beta =\frac{-1-\sqrt{-27 } }{2}$

==> we know that, i²=-1

==> $\beta =\frac{-1-\sqrt{-1\times27 } }{2}$

==> $\beta =\frac{-1-\sqrt{i^{2} \times3\times3\times3 } }{2}$

==> $\beta =\frac{-1-3i\sqrt{3 } }{2}$  

The roots of the equation x²+x+7 are $\alpha =\frac{-1+3i\sqrt{3 } }{2}$   and $\beta =\frac{-1-3i\sqrt{3 } }{2}$