kx² – 2√5 x + 4 = 0. In this eq, find k such that the roots are real and equal and thus find its roots

Question

kx² – 2√5 x + 4 = 0. In this eq, find k such that the roots are real and equal and thus find its roots

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Nevaeh 4 weeks 2021-09-22T00:02:30+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-09-22T00:03:34+00:00

    ◆ kx²– 2√5 x + 4 = 0

    ★ Here, a = k, b = – 2√5 x , c = 4

    ★ Given roots are equal,

    ◆ D = b² – 4ac = 0

    ________________________ \sf

    Solution :

    ⇒ (-2√5)² – 4 × k × 4 = 0

    ⇒ 4 × 5 – 16k = 0

    ⇒ 20 – 16k = 0

    ⇒ – 16k = -20

    ⇒ k = 20/16

    ⇒ k = 5/4

    Hence :

    The required value of K = 5/4

    0
    2021-09-22T00:03:54+00:00

     \large\bf\underline {To \: find:-}

    • we need to find the Value of k.

     \large\bf\underline{Given:-}

    kx² – 2√5x + 4 has two real and equal roots

     \huge\bf\underline{Solution:-}

    If the equation has two real and equal roots then , Discriminant = 0

     \bf \star \:  {b}^{2}  - 4ac = 0

    • ☘ Equation :- kx² – 2√5x + 4

    where,

    • a = k
    • b = – 2√5
    • c = 4
    • b² – 4ac = 0

    ➛ (-2√5)² – 4 × k × 4 = 0

    ➛ 4 × 5 – 16k = 0

    ➛ 20 – 16k = 0

    ➛ – 16k = -20

    ➛ k = 20/16

    ➛ k = 5/4

    Hence,

    • ❥ Value of k is 5/4

    ━━━━━━━━━━━━━━━━━━━━━━━━━

    Now,

    • Equation :- kx² – 2√5x + 4

    ⚘ Putting value of k.

    ➛ 5/4x² – 2√5x + 4

    ➛ (5x² – 8√5x + 16)/4

    ➛ 6x² – 8√5x + 16

    Now,

    Finding roots of the equation :- 6x² – 8√5x + 16 By Middle term splitting method .

    ➛ 5x² – 8√5x + 16

    ➛ 5x² – 4√5 – 4√5 + 16

    ➛ √5x(√5x – 4) -4(√5 – 4)

    ➛ (√5x – 4)(√5x -4)

    ➛ √5x – 4 = 0

    ➛ x = 4/√5 or x = 4/√5

    hence ,

    ❥The roots are 4/√5 and 4/√5

    ━━━━━━━━━━━━━━━━━━━━━━━━━

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