The roots of the polynomial <span><span>x^3 </span>− 2<span>x^2 </span>− 4x + 2</span> are:
<span><span>x1 </span>= 0.42801</span>
<span><span>x2 </span>= −1.51414</span>
<span><span>x3 </span>= 3.08613</span>
x1 and x2 are in the desired interval [-2, 2]
f'(x) = 3x^2 - 4x - 4
so we have:
3x^2 - 4x - 4 = 0
<span>x = ( 4 +- </span><span>√(16 + 48) </span>)/6
x_1 = -4/6 = -0.66
x_ 2 = 2
According to Rolle's theorem, we have one point in between:
x1 = 0.42801 and x2 = −1.51414
where f'(x) = 0, and that is <span>x_1 = -0.66</span>
so we see that Rolle's theorem holds in our function.
Since the co-efficient or "r" is "-3" and "-3", it will simplify to "-6" as -3-3= -6.
then the two constant terms with are "7" and "-12" will simplify to "-5" as 7-12=-5. therefore, the simplest form is -6r -5
hope it helped!
Answer:
it means that the roots of the quadratic equation is real and distinct and that means that 40 is a positive value
Answer:
30.9 cm^2
Step-by-step explanation:
A=(3*2.6)/2+3*(3*6)/2=3.9+27=30.9 cm^2
The solution to the given system of equation is (25/7, 6/7)
<h3>System of equation</h3>
Given the system of equation expressed as:
x= - 4y+7 ........... 1
-2y+3x=9 ...........2
Substitute the equation 1 into 2 into have:
-2y + 3(-4y+7) = 9
-2y + 3(-4y) + 3(7) = 9
-2y - 12y + 21 = 9
Collect the like terms
-14y = 9- 21
-14y = -12
y = 6/7
Substitute y = 6/7 into equation 1;
x =-4y + 7
x = -4(6/7) + 7
x= -24/7 + 7
x = -24+49/7
x = 25/7
Hence the solution to the given system of equation is (25/7, 6/7)
Learn more on system of equation here; brainly.com/question/14323743
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