Solve the problem.
-$$x ^ { 2 } - 8 x + 7 0$$
A) $( 1,7 )$
B) $( - \infty , 1 )$
C) $( 7 , \infty )$
D) $( - \infty , 1 )$ or $( 7 , \infty )$

Question

Solve the problem.
-$$x ^ { 2 } - 8 x + 7 > 0$$
A) $( 1,7 )$
B) $( - \infty , 1 )$
C) $( 7 , \infty )$
D) $( - \infty , 1 )$ or $( 7 , \infty )$

Quizplus · Accepted Answer

To solve the quadratic inequality $x^2 - 8x + 7 > 0$, first factor the quadratic expression. The factors are $(x-1)(x-7)$. Setting each factor equal to zero gives the roots $x = 1$ and $x = 7$. These roots divide the number line into three intervals: $(-\infty, 1)$, $(1, 7)$, and $(7, \infty)$. Testing values from each interval in the original inequality shows that the inequality is satisfied for $x$ values in the intervals $(-\infty, 1)$ and $(7, \infty)$, but not in the interval $(1, 7)$.

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