Question

True or False. The value -2 is lower bound for the zeros of the function shown f(x)=4x^3-12x^2-x+15.

Answer 1

what math u are in?calculus?

Answer 2

Pre Calculus

Answer 3

let us check f(-2) first\[f(-2)=-4*8-12*4+2+15=-63<0\]so its clear that if u plug values of x less than -2 then the value of f will be negative...

Answer 4

Okay....

Answer 5

its a little comparison, u know, because for x<-2\[|4x^3|>15\]\[|12x^2|>|x|\]

Answer 6

so its true right?

Answer 7

Use the upper/lower bounds theorem. http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut39_zero2.htm

"Lower Bound
If you divide a polynomial function f(x) by (x - c), where c < 0, using synthetic division and this yields alternating signs, then c is a lower bound to the real roots of the equation f(x) = 0. Special note that zeros can be either positive or negative.
Note that two things must occur for c to be a lower bound. One is c < 0 or negative. The other is that successive coefficients of the quotient and the remainder have alternating signs."

So use synthetic division to divide by -2, and if you get alternating signs after dividing, it is a lower bound.

Answer 8

Alternating signs meaning - + - + - + -

Answer 9

its true, but it will be better if we use calculus, i dont know which theorem of calculus should be applied here...thats the point...@agent0smith got it :)

Answer 10

You don't need calculus, it's a theorem used in precalc.

Answer 11

yeah i mean precalc :) thank u..i did not know about this theorem. :)

Answer 12

@TinyTasha ignore my solution :)

Answer 13

No prob :) and if you're testing for upper bounds, you want all positives after doing the synthetic division.

Answer 14

Okay thanks.