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

Answer 1

See a solution process below:

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}#
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Answer 2

#x=2,x=3#

#"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]}
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Answer 3

To find the zeros of ( f(x) = 5x^2 - 25x + 30 ), you need to set the function equal to zero and solve for ( x ) using the quadratic formula or factoring:

[ 5x^2 - 25x + 30 = 0 ]

You can either factor the quadratic expression or use the quadratic formula:

Factoring: [ 5x^2 - 25x + 30 = 5(x^2 - 5x + 6) = 5(x - 2)(x - 3) ]

So the zeros are ( x = 2 ) and ( x = 3 ).

Quadratic Formula: [ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} ]

For ( f(x) = 5x^2 - 25x + 30 ), where ( a = 5 ), ( b = -25 ), and ( c = 30 ):

[ x = \frac{{-(-25) \pm \sqrt{{(-25)^2 - 4(5)(30)}}}}{{2(5)}} ] [ x = \frac{{25 \pm \sqrt{{625 - 600}}}}{{10}} ] [ x = \frac{{25 \pm \sqrt{{25}}}}{{10}} ] [ x = \frac{{25 \pm 5}}{{10}} ]

So the solutions are ( x = \frac{{25 + 5}}{{10}} = \frac{{30}}{{10}} = 3 ) and ( x = \frac{{25 - 5}}{{10}} = \frac{{20}}{{10}} = 2 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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