Question

What value of m will make m/3+ 6 -1/9 equal to 0?

Answer 1

Answer:

Answer:

The roots of the equation are equal .

The given equation is ( 4 + m ) x² + ( m + 1 ) x + 1 = 0 .

Comparing with a x² + bx + c = 0 :

a = 4 + m

b = m + 1

c = 1

When the roots of the equation are equal , then we can write that b² = 4 ac  .

Hence :

( m + 1 )² = 4 ( 4 + m ) 1

⇒ m² + 1 + 2 m = 16 + 4 m

⇒ m² - 2 m - 15 = 0

Splitting - 2m into 3 m - 5 m we get :-

⇒ m² + 3 m - 5 m - 15 = 0

Take commons :-

⇒ m ( m + 3 ) - 5 ( m + 3 ) = 0

⇒ ( m - 5 )( m + 3 ) = 0

Either m = 5 .

Or m = - 3

\boxed{\boxed{\bf{\red{Either\:m=5\:or\:m=-3}}}}Eitherm=5orm=−3

Step-by-step explanation:

It is not mentioned in the question .

The roots of the equation will be equal .

When roots are equal :

b² = 4 ac

When roots are unequal and real :-

b² > 4 ac

When roots are complex :

b² < 4 ac

Apply the above formula and then find the value of m :) .

Answer 2

Mx−2y=9

On comparing the above equation with ax+by+c=0

a

1

=M,b

1

=−2,c

1

=9

4x−y=7

a

2

=4,b

2

=−1,c

2

=7

Condition for unique solution is

a

2

a

1



=

b

2

b

1

⇒

4

M



=

+1

+2

⇒M



=

1

8

⇒M



=8

∴ M can have all real values except 8