Matematika

Pertanyaan

akar-akar persamaan kuadrat 2x^2 - 3x + 5 = 0 adalah α dan β. nilai dari α/β + β/a = ....
a. -12/10
b. - 11/10
c. -9/10
d. -7/10
e. - 3/10

mohon bantuannya ^^ dan terimakasih atas bantuannya :)

1 Jawaban

  • 2x² - 3x + 5 = 0 >> a=2, b=-3, c=5

    α+β = -b/a
           = -(-3)/2
           = 3/2

    α.β = c/a
          = 5/2

    α/β + β/a = (α²+β²)/αβ
                  = [(α+β)²-2αβ]/αβ
                  = [(3/2)²-2(5/2)]/(5/2)
                  = [(9/4)-5]/(5/2)
                  = [(9/4)-(20/4)]/(5/2)
                  = (-11/4)/(5/2)
                  = -11/4 x 2/5
                  = -11/10                       (b)


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