Quadratic Equations in One Unknown

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Quadratic Equations in One Unknown
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What is quadratic equation in one unknown?
Quadratic polynomial in x
x 2 ? 5x 6
Polynomials of degree 2
8x 2 2x ? 3
Quadratic equations in x
x 2 ? 5x 6 0
Equations of degree 2
8x 2 2x ? 3 0
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General form of quadratic equations in one unknown
ax2 bx c 0

• If a 0, the equation becomes a linear equation
  bx c 0

• We usually keep a positive.

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Are the following quadratic equations?
Yes. By transposing terms, 2x2 5x ? 3 0
2x2 5x 3
Yes. By expanding the equation, x2 x 3 0
x(x 1) 3 0
Yes. By expanding and transposing terms,
x2 ? 4x 3 0
(x ? 2)2 1
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Roots of a quadratic equation
A root of an equation is a value of x that
satisfies the equation. For example, 3 is a root
of the equation x2 ? 9 0.
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Follow-up question
Is ?1 a root of the equation x 2 ? 5x ? 6 0?
Substitute x ?1 into the equation,
L.H.S.
(?1)2 ? 5(?1) ? 6
0
R.H.S.
? ?1 is a root of the equation.