Find integer bounds for the roots of the following equation. $$x ^ { 2 } - 2 x - 7 = 0$$
A) $- 2,4$
B) $- 1,3$
C) $- 2,6$
D) $- 3,3$
E) none of these

Question

Quizplus · Accepted Answer

The roots of the quadratic equation can be found using the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. For the equation $x^2 - 2x - 7 = 0$, $a = 1$, $b = -2$, and $c = -7$. The discriminant $b^2 - 4ac = 4 + 28 = 32$, so the roots are $x = \frac{2 \pm \sqrt{32}}{2}$. Simplifying gives $x = 1 \pm \sqrt{8}$, which is approximately $1 \pm 2.828$. Thus, the roots are approximately $-1.828$ and $3.828$, so the integer bounds are $-2$ and $4$.

Find Integer Bounds for the Roots of the Following Equation x2−2x−7=0x ^ { 2 } - 2 x - 7 = 0x2−2x−7=0

Find Integer Bounds for the Roots of the Following Equation $x ^ { 2 } - 2 x - 7 = 0$