Trish is solving for the zeros of the quadratic function f(x) = 2x2 – 3x + 3. x = x = x = x = Did Trish find the correct zeros of this function? Explain. Yes, those are the two real number zeros. No, the two real number zeros are . No, the two real number zeros are . No, the function has no real number zeros.

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calculista calculista · Answer 1 · 2018-12-03T18:12:19+01:00

Answer:

No, the function has no real number zeros

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]f(x)=2x^{2} -3x+3[/tex]

equate the function to zero

so

[tex]2x^{2}-3x+3=0[/tex]

[tex]a=2\\b=-3\\c=3[/tex]

substitute in the formula

[tex]x=\frac{3(+/-)\sqrt{(-3)^{2}-4(2)(3)}} {2(2)}[/tex]

[tex]x=\frac{3(+/-)\sqrt{9-24}} {4}[/tex]

[tex]x=\frac{3(+/-)\sqrt{-15}} {4}[/tex]

remember that

[tex]i=\sqrt{-1}[/tex]

[tex]x=\frac{3+\sqrt{15}i} {4}[/tex]

[tex]x=\frac{3-\sqrt{15}i} {4}[/tex]

The function has no real number zeros

abidemiokin abidemiokin · Answer 2 · 2022-04-25T17:09:45+02:00

Since the discriminant is less than 0, hence the function has no real number zeros.

The discriminant is used to determine the nature of a function. It is expressed as:

D = b^2 - 4ac

Given the quadratic function f(x) = 2x^2 – 3x + 3

a = 2

b = -3
c = 3

Substitute into the expression to have:

D = (-3)^2 - 4(2)(3)
D = 9 - 24
D = -15

Since the discriminant is less than 0, hence the function has no real number zeros.

Learn more on discriminant here: https://brainly.com/question/2507588