Question

Root roots of 2x² + mx + 16 = 0 are a and β. If a = 2 β and a, β are positive, the m value

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Answer 1

Root roots of 2x² + mx + 16 = 0 are a and β. If a = 2 β and a, β are positive, the m value that satisfies is -12.

DISCUSSION :

If α and β are the ax² + bx + c = 0 roots, then it applies

1. α + β = -b / a

2. α x β = c / a

Known :

2x² + mx + 16 = 0 equation

a = 2

b = m

c = 16

a = 2β and a, β are positive

Asked: m value?

Answer:

Β value:

  α x β = c / a

  α x β = 16/2

2β x β = 8

     2β² = 8

       β² = 8/2

       β² = 4

        β = 2

  α + β = -b / a

  α + β = -m / 2

2β + β = -m / 2

      3β = -m / 2

For β = 2, then the value of m:

   3β = -m / 2

3 (2) = -m / 2

     6 = -m / 2

  -m = 6 x 2

  -m = 12

   m = -12

Answer 2

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