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

Question

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

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2 months 2021-10-09T19:04:01+00:00 2 Answers 0 views 0

1. 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

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
2. ## Given :

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

• Value of m

• 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

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 .