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

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    0
    2021-10-09T19:05:12+00:00

    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
    0
    2021-10-09T19:05:18+00:00

    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 .

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