For what value of k are the roots of the quadratic equation kx²+ 4x+ 1=0 equals and reals.” ​

Question

For what value of k are the roots of the quadratic
equation kx²+ 4x+ 1=0 equals and reals.”
​

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Trúc Chi 4 years 2021-07-19T23:48:18+00:00 1 Answers 28 views 0

Answers ( )

  1. danthu
    0
    2021-07-19T23:49:21+00:00
    Reply

    Answer:

    k ≥ 4

    Step-by-step explanation:

    A Quadratic equation is given to us and we need to find out the value of k for which the equation has real roots. The given equation is ,

    \rm\implies kx^2 +4x +1=0

    With respect to Standard form of Quadratic equation :-

    \rm\implies ax^+bx+c=0

    For real roots ,

    \rm\implies Discriminant = b^2-4ac\geq 0

    Substitute the respective values ,

    \rm\implies b^2-4ac \geq 0\\

    \rm\implies 4^2 - 4(k)(1) \geq 0 \\

    Simplify the LHS ,

    \rm\implies 16 - 4k \geq 0 \\

    Add 4k both sides ,

    \rm\implies 4k\geq 16

    Divide both sides by 4 ,

    \rm\implies \boxed{\blue{\rm k \geq 4}}

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