Question

The quadratic equation root5x sqrt +2mx +m/root 5 has two equal roots. find the value of m​

Answer 1

Given :

• P(x) = √5 x² + 2mx + m/√5
• Roots are equal .

To find :

• Value of m

Answer :

• m = 1

Solution :

Here in the given equation :

• a = √5
• b = 2m
• c = m/√5

Finding the discriminant of the equation :

D = b² - 4ac

D= (2m)² - 4 × √5 × m / √5

D = 4m² - 4m

For any equation to have equal roots , the value of discriminant must be equal to 0 .

•°• 0 = 4m² - 4m

0 = 4m ( m - 1)

0 = m - 1

0 + 1 = m

$\boxed{\tt m = 1}$

Now the final equation becomes :

P(x) = √5 x² + 2(1)x + (1)/√5

P(x) = √5 x² + 2x + 1/√5

A quadratic equation is the one that has degree of polynomial equals to 2 . The number of degree of polynomial gives the number of roots of the equation .

Answer 2

Given ,

The polynomial √5(x)² + 2mx + m/√5 has two equal roots

Here ,

a = √5

b = 2m

c = m/√5

We know that ,

If polynomial has two equal real , then

$\boxed{ \sf{Discriminant = 0 \: i.e \: (b)² - 4ac = 0}}$

Thus ,

(2m)² - 4 × √5 × m/√5 = 0

4m² - 4m = 0

4m(m - 1) = 0

4m = 0 or m - 1 = 0

m = 0 or m = 1

Therefore ,

• The value of m will be 1 or 0