How do you find the zeros of #f(x)=5x^2-25x+30#?

2 Answers
Nov 12, 2017

Answer:

See a solution process below:

Explanation:

We can factor this function as:

#f(x) = (5x - 15)(x - 2)#

To find the zeros we can solve each term on the right side of the function for #0#:

Solution 1:

#5x - 15 = 0#

#5x - 15 + color(red)(15) = 0 + color(red)(15)#

#5x - 0 = 15#

#5x = 15#

#(5x)/color(red)(5) = 15/color(red)(5)#

#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 3#

#x = 3#

Solution 2:

#x - 2 = 0#

#x - 2 + color(red)(2) = 0 + color(red)(2)#

#x - 0 = 2#

#x = 2#

The Solutions Are: #x = {2, 3}#

Nov 12, 2017

Answer:

#x=2,x=3#

Explanation:

#"to calculate the zeros set "f(x)=0#

#rArr5x^2-25x+30=0larrcolor(blue)"factorise to solve"#

#rArr5(x^2-5x+6)=0#

#"the factors of + 6 which sum to - 5 are -2 and - 3"#

#rArr5(x-2)(x-3)=0#

#"equate each factor to zero and solve for x"#

#x-2=0rArrx=2#

#x-3=0rArrx=3#

#"the zeros are "x=2,x=3#
graph{(y-x^2+5x-6)((x-2)^2+y^2-0.07)((x-3)^2+y^2-0.07)=0 [-10, 10, -5, 5]}