f(x) = −4x3 + 8x2 + 21x
Find the zeros of the polynomial

Question

f(x) = −4x3 + 8x2 + 21x
Find the zeros of the polynomial

rsadhvika · Answer

start by factoring out the gcf

anonymous · Answer

2

rsadhvika · Answer

2 is not a factor of 21
check again

and wat about x ?

jack1 · Answer

$$f(x) = −4x^3 + 8x^2 + 21x$$
first factor the equation
so x is a factor of everything in the above equation, so factor that out first
$$f(x) = −4x^3 + 8x^2 + 21x \rightarrow \rightarrow \rightarrow x(−4x^2 + 8x + 21x)$$

jack1 · Answer

sorry, becomes : $$f(x) = x(−4x^2+8x+21)$$

jack1 · Answer

$$f(x) = x(−4x^2+8x+21)$$
further factors down to...?
factors of 21 = 1 and 21 or 7 and 3
factors of -4x^2 are 2x and -2x or 4x and -x

jack1 · Answer

which combination would add to 8x...?

so 7 and 3
and 2x and -2x

in $$f(x) = x(−4x^2+8x+21)$$
$$f(x) = -x(2x - 7)(2x + 3)$$

jack1 · Answer

so your zeros are at f(x) = 0
$$f(x) = -x(2x - 7)(2x+3)$$
$$ 0 = -x(2x - 7)(2x+3)$$
so call the brackets A and B
now (bear with me here) there are 3 options for the zeros

either x = 0 [as 0 times ( A ) times ( B ) ]= 0
or  A = zero {[as x times ( 0 ) times ( B ) ]= 0}
or  B = zero {[as x times ( A ) times ( 0 ) ]= 0}

jack1 · Answer

so the zeros are at:

x = 0     [as 0 times ( A ) times ( B ) ]= 0

or  A = zero {[as x times ( 0 ) times ( B ) ]= 0}
so if A = 0,    (2x -7) =0
2x - 7 = 0
2x = 7
x = 7/2 = 3.5

or  B = zero {[as x times ( A ) times ( 0 ) ]= 0}
so if A = 0,    (2x +3) =0
2x +3 = 0
2x = -3
x = -3/2 = -1.5

jack1 · Answer

...sorry it's so long winded, but does that all make sense dude?