Answer:
p=13, k = 3.25
Step-by-step explanation:
First, determine p:
[tex]2x^2+px+15=0\\x=-5:\\2(-5)^2+p(-5)+15=0\\-5p+65=0\\\implies p=13[/tex]
Use this value in the second equation
[tex]13(x^2+x)+k=0[/tex]
and write the condition for that equation having equal roots, i.e., its determinant must equal 0:
[tex]13x^2+13x+k=0\\D=b^2-4ac=13^2-4\cdot13\cdot k=0\\52k=169\implies k = 3.25[/tex]
