Question

F(x)=(5x+1)(4x−8)(x+6)f, left parenthesis, x, right parenthesis, equals, left parenthesis, 5, x, plus, 1, right parenthesis, left parenthesis, 4, x, minus, 8, right parenthesis, left parenthesis, x, plus, 6, right parenthesis has zeros at x=-6x=−6x, equals, minus, 6, x=-\dfrac{1}{5}x=− 5 1 ​ x, equals, minus, start fraction, 1, divided by, 5, end fraction, and x=2x=2x, equals, 2

Answer 1

Answer:

$x=-\frac{1}{5} \:or \: x=2 \:or\: x=-6$

Step-by-step explanation:

Given $f(x)=(5x+1)(4x-8)(x+6)$

The zeros of the polynomial function are the point where the function f(x) equals zero.

$f(x)=(5x+1)(4x-8)(x+6)=0$

If abc=0, then a=0 or b=0 or c=0

Therefore:

$(5x+1)(4x-8)(x+6)=0 \:means\\5x+1=0 \:or \: 4x-8=0 \:or\: x+6=0\\5x=-1 \:or \: 4x=8 \:or\: x=-6\\x=-\frac{1}{5} \:or \: x=2 \:or\: x=-6$