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Chapter 10: Q. 3 (page 700)

For what numbers x is6-x鈮�x2?

Short Answer

Expert verified

The solution set is[-3,2]

Step by step solution

01

Step 1. Given information

The given inequality is6-x鈮�x2

02

Step 2. Calculation

Rewrite the given inequality,

x2+x-6鈮�0

Find the y-intercept of the function f(x)=x2+x-6by substituting x=0

f(0)=(0)2+0-6=-6

Factorize the equation as follows,

x2+x-6=0(x-2)(x+3)=0x=2,-3

Thus, y-intercept is -6and x-intercepts are2,-3

03

Step 3. Calculation

Compare the given function with the standard form ax2+bx+c=0,

a=1,b=1,c=-6

The x-coordinate of the vertex is as follows,

-b2a=-12

Find the y-coordinate of the vertex,

f(-12)=-122-12+6=14-12+6=1-2-244=-254

Graph the function with vertex -12,-254and the points (-3,0),(0,-6)and(2,0)

Thus, the solution set isx|-3鈮�x鈮�2

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