Respuesta :

The value of 'k' in the quadratic Equation    [tex]4x^{2}+kx+4=0[/tex] having one rational solution is k is 8.

What is a Quadratic Equation?

  • Quadratic equations are the polynomial equations of degree 2 in one variable of the type [tex]f(x) = ax^{2} + bx + c = 0[/tex] where a, b, c, ∈ R and a ≠ 0.
  • The standard form of a quadratic equation is [tex]ax^{2} + bx + c = 0[/tex] .

Here, the given equation is  [tex]4x^{2}+kx+4=0[/tex]

By comparing the given equation with the standard form of the quadratic equation we get,

a = 4

b = k

c = 4

The given quadratic is having one rational solution, which means [tex]b^{2} -4ac=0[/tex]

Therefore,

[tex]k^{2} -4 \times 4\times4=0\\k^{2} -64=0\\k^{2} =64\\k=\sqrt{64} \\k=8[/tex]

Therefore, the value of k is 8.

Learn more about the quadratic equation is https://brainly.com/question/8649555

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