Question

Identify the interval(s) on which the function y = 2x^2 - 8x - 10 is positive.

Answer 1

Given:

$y=2x^2-8x-10$

To find:

The interval(s) on which the given function is positive.

Solution:

We have,

$y=2x^2-8x-10$

$y=2(x^2-4x-5)$

$y=2(x^2-5x+x-5)$

$y=2(x(x-5)+1(x-5))$

$y=2(x+1)(x-5)$

For zeroes, $y=0$

$2(x+1)(x-5)=0$

$x=-1,x=5$

-1 and 5 divide the number line in three parts $(-\infty , -1),(-1,5),(5,\infty )$.

Interval        Selected Value      $y=2(x+1)(x-5)$                      Sign

$(-\infty,-1)$                -2                  $y=2(-2+1)(-2-5)=14$           +

$(-1,5)$                     0                   $y=2(0+1)(0-5)=-10$              -

$(5,\infty)$                       6                  $y=2(6+1)(6-5)=14$                 +

So, the function is positive for interval $(-\infty,-1)$ and $(5,\infty)$.

We can say that the function is positive for interval x < -1 and x > 5.

Therefore, the correct option is B.