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# Quadratic Equations

Quadratic Equation: Eqn equivalent to

where A, B, C real, A ≠ 0

This 2^{nd} degree eqn is the standard form.

**Solving by Factoring
**If can factor left side, then can solve by Zero-

Product Property which says:

If ab = 0 then either a = 0 or b = 0 or both

In general, quadratic eqn has 2 roots.

If both factors in factorization are identical,

both solns same & root has multiplicity 2,

called double root.

e.g.

**Square Root Method
**Some eqns solved simply by taking square root

e.g. If x

^{2}= p and p ≥ 0, then

e.g.

(double root)

**Completing the Square
**If left side of eqn is perfect square, can solve it.

Adjust left side to be perfect square, change right

side appropriately

e.g.

42: x

^{2}– 6x = 13

Strategy:

If x^{2} has coefficient ≠ 1, divide both sides by it

Start with x^{2} + Bx + C = 0

Move C to other side x^{2} + Bx = C

Add to both sides

Use Square Root Method to solve eqn.

e.g.

46: 2x^{2} – 3x – 1 = 0

**Quadratic Formula**

For general quadratic (with A ≠ 0)

ax^{2} + bx + c = 0

Discriminant: (b^{2} – 4ac)

If (b^{2} – 4ac) > 0 then 2 real solutions

If (b^{2} – 4ac) = 0 then 1 real solution

If (b^{2} – 4ac) < 0 then no real solutions

53: 4y^{2} – y + 2 = 0no
real solns

59: 9t^{2} – 6t + 1 = 0
x = 1/3 (double root)

**Assignment:
Do problems for 1.2
Read ยง1.3**