Saturday

February 28, 2015

February 28, 2015

Posted by **Jayden Haddy** on Sunday, August 11, 2013 at 12:52am.

- maths -
**Bosnian**, Sunday, August 11, 2013 at 2:01amIn quadratic equation:

a x ^ 2 + b x + c

expresion :

delta = b ^ 2 - 4 a c

is called the Discriminant

When delta > 0

There is two real root

When delta = 0

There is 2 equal real roots. ( The root is repeated. )

When delta < 0

There are two complex ( unreal ) roots.

In this case :

a = m ^ 2 + n ^ 2

b = - 2 ( m + n )

c = 2

delta = b ^ 2 - 4 ac

delta = [ - 2 ( m + n ) ] ^ 2 - 4 * ( m ^ 2 + n ^ 2 ) * 2

delta = 4 * ( m + n ) ^ 2 - 8 * ( m ^ 2 + n ^ 2 )

delta = 4 * ( m ^ 2 + 2 m n + n ^ 2 ) - 8 m ^ 2 - 8 n ^ 2

delta = 4 m ^ 2 + 8 m n + 4 n ^ 2 - 8 m ^ 2 - 8 n ^ 2

delta = - 4 m ^ 2 + 8 m n - 4 n ^ 2

delta = - 4 ( m ^ 2 - 2 m n + n )

delta = - 4 ( m - n ) ^ 2

Becouse : ( m - n ) ^ 2 = m ^ 2 - 2 * m n + n ^ 2

So delta = - 4 ( m - n ) ^ 2

When m > n

( m - n ) are positive

Square of positive number are positive number.

- 4 * positive number are negative number

When m < n

( m - n ) are negative

Square of negative number are positive number.

- 4 * positive number are negative number

This mean when m is not equal to n the Disciminant is always negative , and your equation always have two unreal roots.

________________________________________

Remark :

delta is greek letter delta ( Like triangle).

________________________________________

**Answer this Question**

**Related Questions**

maths - if a, b,c are real numbers and not all equal, prove that the equation (c...

maths Please help!!!!! - if a, b,c are real numbers and not all equal, prove ...

maths - If the sum of the squares of the roots of the quadratic equation ax^2 + ...

maths - find the roots of the equation X(square)+7x equal to 0.(b)write down the...

maths - Prove that if p and q are rational and p is not equal to 0, the roots ...

maths - If the ratio of the roots of the quadratic equation ax^2 + bx +c =0 is m...

maths - If a,b and c € R, then prove that the roots of the eqn 1/(x-a) + 1/(x-b...

maths - If the roots of the eqn 1/(x+p) + 1/(x+p) = 1/r are equal in magnitude ...

maths - Prove that if p and q are rational and p is not equal to 0, the roots of...

Please help! Maths - For what value of K will the equation 3x^2- 4x-(1+K)= 0 ...