Question

Consider the following equation

Answer 1

Answer:

The negative solution is between -3 and -2

The positive solution is between 11 and 13

Step-by-step explanation:

we have

$0=x^{2} -10x-27$

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2} -10x-27=0$  

so

$a=1\\b=-10\\c=-27$

substitute in the formula

$x=\frac{10(+/-)\sqrt{-10^{2}-4(1)(-27)}} {2(1)}$

$x=\frac{10(+/-)\sqrt{208}} {2}$

$x=\frac{10(+)\sqrt{208}} {2}=12.21$

$x=\frac{10(-)\sqrt{208}} {2}=-2.21$

therefore

The negative solution is between -3 and -2

The positive solution is between 11 and 13

Answer 2

Answer:

Negative solution is between -3 and -2

Positive solution is between 12 and 13

Step-by-step explanation: