For what values of x, the inequality is true? x^2-4x=<12

Expert Answers
hala718 eNotes educator| Certified Educator

x^2-4x=<12

==> x^2-4x-12=<0

First let us factorize:

==> (x-6)(x+2)=<0

==> x-6=<0 and (x+2)=>0

==> x=<6  and x=>-2   

==> x belongs to [-2,6]

OR (x-6)=>0  and (x+2)=<0

==> x=>6    and  x=<-2   which is impossible.

Then the solution is x belongs to [-2,6]

giorgiana1976 | Student

First of all, we'll solve the qudratic equation:

x^2 -4x -12 = 0

After that, to find out the roots of the equation, we'll use the quadratic formula:

x1 = [-b + sqrt(b^2 - 4ac)]/2a, where a=1, b=-4, c =-12

x2 = [-b + sqrt(b^2 - 4ac)]/2a,

after calculation

x1=6, x2=-2

We know that the expression is negative between the roots, because the values of function have the opposite sign of the "a" coefficient, which is positive.

The inequality is negative when x belongs to the interval [-2,6].

neela | Student

x^2-4x<=12 is theinequality. To detrmine x for which the inequatlity holds:

Solution:

We shift  aubtract 12  from both sides , then the equality becoms:

x^2-4x-12 < 0.  Or

x^2-6x+2x-12 <0. Or

x(x-6)+2(x-6) < 0. Or

(x-6)(x+2) < 0. For this product of the factors (x-6)(x+2) should be negative. Or  x should lie between the roots -2 and 6.