Answer:
a) k = -7
b) x = -5/4
Step-by-step explanation:
[tex]4x^2+kx-15=0[/tex]
Substitute [tex]x=3[/tex] and solve for [tex]k[/tex]:
[tex]4(3^2)+3k-15=0\\36+3k-15=0\\3k=-21\implies k=\boxed{-7}[/tex]
Plugging [tex]k[/tex] back in to [tex]4x^2+kx-15=0[/tex]:
[tex]4x^2-7k-15=0[/tex]
Factor:
[tex](4x+5)(x-3)=0[/tex]
[tex]4x+5=0\implies x=\boxed{-\frac{5}{4}}[/tex]
