# maths

posted by .

prove that if m is not equal to n, the equation (m^2+n^2)x^2 - 2(m+n)x + 2=0 has unreal roots.

• maths -

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).

________________________________________

## Similar Questions

1. ### maths

find the roots of the equation X(square)+7x equal to 0.(b)write down the equation whose roots are -2 and 5. I will be happy to critique your thinking. Write the equation, and solve. In the second, hint: (x+2) is one factor.
2. ### Algebra

The equation x^2+px+q=0, q cannot be equal to 0, has two unequal roots such that the squares of the roots are the same as the two roots. Calculate the product pq. I think the obvious root would be one but the second roots i just can't …
3. ### maths

Prove that if p and q are rational and p is not equal to 0, the roots of the quadratic equations p x(square) + 2qx -p +2q = 0.
4. ### maths

Prove that if p and q are rational and p is not equal to 0, the roots of the quadratic equations p x(square) + 2qx -p +2q = 0 are rational.
5. ### maths

if a, b,c are real numbers and not all equal, prove that the equation (c-a)x^2 -2(a-b)x + (b+c) = 0 has unequal real roots

if a, b,c are real numbers and not all equal, prove that the equation (c-a)x^2 -2(a-b)x + (b+c) = 0 has unequal real roots
7. ### maths

If the ratio of the roots of the quadratic equation ax^2 + bx +c =0 is m:n prove that mnb^2=(m+n)^2 ac
8. ### maths

If the sum of the squares of the roots of the quadratic equation ax^2 + bx + c = 0 is m:n, prove that b^2= 2ac + 4a^2 I really have no idea how to prove it so pls help
9. ### maths

If the roots of the eqn 1/(x+p) + 1/(x+p) = 1/r are equal in magnitude but opposite in sign, show that p+r=2r and that the product of the roots is equal to (-1/2) (p²+q²)
10. ### maths

If a,b and c € R, then prove that the roots of the eqn 1/(x-a) + 1/(x-b) + 1/(x-c) =0 are always real and cannot have roots if a=b=c.

More Similar Questions