Respuesta :

Dead3ill

Answer:

k = +10 or -10

Step-by-step explanation:

It's given in the question that the roots of the eqn. are real and equal. So , the discriminant of the eqn. should be equal to 0.

[tex] = > {b}^{2} - 4ac = 0[/tex]

[tex] = > {( - 2k)}^{2} - 4 \times 5 \times 20 = 0[/tex]

[tex] = > 4 {k}^{2} - 400 = 0[/tex]

[tex] = > 4( {k}^{2} - 100) = 0[/tex]

[tex] = > {k}^{2} - 100 = 0[/tex]

[tex] = > k = \sqrt{100} = + 10 \: or \: - 10[/tex]

Step-by-step explanation:

Given Equation

5x-2kx+20=0

  • If it has real and equal roots then

[tex]\boxed{\sf \longrightarrow D=0 }[/tex]

  • Substitute the values

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow b^2-4ac=0 [/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow (-2k)^2-4\times 5\times 20=0 [/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow 4k^2-20\times 20=0 [/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow 4k^2-400=0[/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow 4k^2=400 [/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow k^2=\dfrac {400}{4}[/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow k^2=100 [/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow k=\sqrt{100}[/tex]

[tex]\\\qquad\quad\displaystyle\sf {:}\longrightarrow k=10 [/tex]

[tex]\therefore\sf k=10 [/tex]

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