Writing Equations Given Roots

​DISCRIMINANT

The Radicand ​(b²-4ac) in the quadratic formula

​USING THE DISCRIMINANT

1. If b²-4ac is greater than 0 the equation has two real solutions. Both will be rational if the discriminant is a perfect square or irrational.

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2. ​If b²-4ac is equal to 0, the equation has only one solution which will ne a rational number.

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3. If b²-4ac is​ less than 0, the equation has no real number solution.

Example:

​1. 16x²-8x+1=0​

b²-4ac =​ (-8)²-4(16)(1)

=​ 64 - 64

= 0

Therefore, the discriminant is 0.

Hence, the equation has only one solution. ​

​RELATION OF ROOTS

The relations that exist between the roots of a quadratic equation which can be used in checking the validity of the roots can be of best use in deriving the quadratic equation.

​RELATION OF ROOTS

1. The sum of the roots is the additive​ inverse of the quotient of b and a.

   1. r₁+r₂ = - b/a​

2. The product of the roots is the quotient of c and a​.

   1. ​r₁-r₂ = c/a​

Example:

​1. x²- 2x -8 =0​

solution: (x+2)(x-4) = 0

x+2 = 0 or x-4 = 0

​​root 1 = x+2

root 2 = x-4​

Example:

​1. x²- 2x -8 =0​

r₁+r₂ = - b/a​ and r₁-r₂ = c/a​

(2)+(-4) = -2/1​ (2)(-4) = -8/1

-2 = -2 True -8 = -8 True​

By Kristine Jardio