Determina el valor que deb tener k para qu cumpla la condicion dada se cumpla a?

<img src="https://tex.z-dn.net/?f=Hola~~%20~%5Cmathbf%7BVictor%7D%20%5C%5C%20%20%5C%5C%20x%5C%C2%B2-kx%2B27%3D0%20%5C%5C%20De~la~forma%20%5C%5C%20%5Cboxed%7Ba%20x%5E%7B2%7D%20%2Bbx%2Bc%7D%20%7D%5Cbegin%7Bcases%7D%5Cunderbrace%7Bsuma~de~raizes~%7D%20%5C%5C%20~~x_1%2Bx_2%3D%20%5Cfrac%7B-b%7D%7Ba%7D%20%20%5C%5C%20%20%5C%5C%20%5Cunderbrace%7Bproducto~de~raizes%7D%20%5C%5C%20~~~~x_1.x_2%3D%20%5Cfrac%7Bc%7D%7Ba%7D%20%5Cend%7Bcases%7D%20%5C%5C%20%20%5C%5C%20Y~nos~indica~una~raiz~es~triple~de~la~otra~osea%3A%20%5C%5C%20%20%5C%5C%20x_1%3Dx_1%20%5C%5C%20x_2%3D3x_1%20%5C%5C%20%20%5C%5C%20Com~base~a%20~eso~resolvemos~%27%27k%27%27%5C%5C%20%20%5C%5C%20%20" />

<img src="https://tex.z-dn.net/?f=Del~producto~de~raizes~tenemos%3A%20%5C%5C%20x_1.x_2%3D%20%5Cfrac%7Bc%7D%7Ba%7D%20~~--%5C%20%5Ctextgreater%20%5C%20donde%5Cbegin%7Bcases%7Dc%3D27%20%5C%5C%20a%3D1%20%5C%5C%20x_2%3D3x_1%5Cend%7Bcases%7D%20%20%5C%5C%20%20%5C%5C%20reemplazando~tenemos%3A%20%5C%5C%20%20x_1.3x_1%3D%20%5Cfrac%7B27%7D%7B1%7D%20%5C%5C%20%20%5C%5C%203%28x_1%29%5C%C2%B2%3D27%20%5C%5C%20%20%5C%5C%20%28x_1%29%5C%C2%B2%3D9%20%5C%5C%20%20%5C%5C%20%5Cboxed%7Bx_1%3D%5Cpm%203%7D%20~~--%5C%20%5Ctextgreater%20%5C%20%27%27x_1%27%27~puede~tomar~%5B%2B3~~0%27%20~-3%5D%20%5C%5C%20%20%5C%5C%20Entonces~como~indica~las~raizes~seriam%20%5C%5C%20x_1%3D%5Cpm3%20%5C%5C%20x_2%3D%5Cpm9%20%5C%5C%20%20%5C%5C%20%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%5C%5C%20%20%5C%5C%20%20%5C%5C%20." />

<img src="https://tex.z-dn.net/?f=%20Calculemos~el~valor~de~%27%27k%27%27%2C%20para~lo~cual~usaremos~suma~de%20%5C%5C%20las~raizes~veamos%3A%20%5C%5C%20%20%5C%5C%20x_1%2Bx_2%3D%20%5Cfrac%7B-b%7D%7Ba%7D~~--%5C%20%5Ctextgreater%20%5C%20donde~%5Cbegin%7Bcases%7Dx_1%3D%5Cpm3%20%5C%5C%20x_2%3D%5Cpm9%20%5C%5C%20b%3D-k%20%5C%5C%20a%3D1%5Cend%7Bcases%7D%20%20%5C%5C%20%20%5C%5C%20reemplazando%20~usemos~valores~de~las~raizes~los~positivos%20%5C%5C%203%2B9%3D%20%5Cfrac%7B-%28-k%29%7D%7B1%7D%20%20%5C%5C%20%20%5C%5C%20%5Cboxed%7B%5Cboxed%7Bk%3D%2B12~~~~o%27~~~k%3D-12%7D%7D%20%5C%5C%20%20%5C%5C%20%5Cmathbb%7Bxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx%7D%5C%5C~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Saludos%21%21%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20" />.