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2.) Which of the following expressions represents a quadratic equation?
I. (x+5) (x+5) =3
II. x2 = -2x + 5
III. 2x - 1 = 3x + 7
a. I only
b. III only
c. ll only
d. I and II​

Sagot :

KAntoineDoixidn

QUADRATIC EQUATION

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Question:

Which of the following expressions represents a quadratic equation?

I. (x+5) (x+5) = 3

II. x2 = -2x + 5

III. 2x - 1 = 3x + 7

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Answer:

D. I and II

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Why?

  • Choice I

[tex] \sf {(x + 5)}^{2} = 3 \\ \sf {x}^{2} + 10x + 25 = 3 \\ \sf {x}^{2} + 10x + 25 - 3 = 0 \\ \boxed{\sf {x}^{2} + 10x + 22 = 0}[/tex]

This is Quadratic Equation, with the root of...

[tex] \sf x = - 5 ± \sqrt{3} [/tex]

.

.

  • Choice II

[tex] \sf{x}^{2} = - 2x + 5 \\ \boxed{ \sf{x}^{2} + 2x - 5 = 0}[/tex]

This is Quadratic Equation, with the root of...

[tex] \sf x = - 1 ± \sqrt{6} [/tex]

.

.

  • Choice III

[tex] \sf2x - 1 = 3x + 7 \\ \sf2x - 3x = 7 + 1 \\ \sf - x = 8 \\ \boxed{\sf x = - 8}[/tex]

This is NOT Quadratic Equation, the value of x is -8

.

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