If roots of quadratic equation real and equal find k k(2x-5)=x^2-4

Question

If roots of quadratic equation real and equal find k k(2x-5)=x^2-4

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Amara 2 weeks 2021-09-07T14:26:51+00:00 1 Answer 0 views 0

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    2021-09-07T14:28:48+00:00

    Answer:

    Step-by-step explanation:

    k²(2x -5 ) = x² -4

    2xk²- 5k² = x² – 4

    x² -2k²x + 5k²-4 = 0

    Compare Ax²+Bx + C =0

    A = 1 , B = -2k² , C = 5k²-4

    And roots are equal then conditions are

    B² – 4AC = 0

    (-2k²)² – 4×1×(5k²-4) = 0

    4k⁴ – 20k²+16 = 0

    K⁴ -5k² +4 = 0

    k⁴ -4k²-k² +4 = 0

    k²(k²-4) – 1 (k²-4) = 0

    (k²-4) (k²-1) = 0

    Now, k²-4 = 0 or k²-1 = 0

    k² = 4 or k² = 1

    k = +2 and -2 or k = +1 and -1

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