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How do you solve #3x^2-10x+3=0#?

Answer 1

Eva Abramson

See a solution process below:

We can factor the left side of the equation as:

#(3x - 1)(x - 3) = 0#

Now, solve each term on the left side of the equation for #0#

Solution 1:

#3x - 1 = 0#

#3x - 1 + color(red)(1) = 0 + color(red)(1)#

#3x - 0 = 1#

#3x = 1#

#(3x)/color(red)(3) = 1/color(red)(3)#

#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 1/3#

#x = 1/3#

Solution 3:

#x - 3 = 0#

#x - 1 + color(red)(3) = 0 + color(red)(3)#

#x - 0 = 3#

#x = 3#

The Solution Set Is:

#x = {1/3, 3}#

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Answer 2

Avery Alexander

You can solve the quadratic equation 3x^2 - 10x + 3 = 0 using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

where a = 3, b = -10, and c = 3.

Plugging in the values, you get:

x = (10 ± √((-10)^2 - 4(3)(3))) / (2*3)

Simplify under the square root:

x = (10 ± √(100 - 36)) / 6

x = (10 ± √64) / 6

x = (10 ± 8) / 6

This gives you two possible solutions:

x₁ = (10 + 8) / 6 = 18 / 6 = 3

x₂ = (10 - 8) / 6 = 2 / 6 = 1/3

So, the solutions to the equation are x = 3 and x = 1/3.

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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.