Answer:
[tex]$k=\frac{7}{4} $[/tex]
Step-by-step explanation:
[tex]2x^2+px-15=0[/tex]
Once [tex]x=-5[/tex]
[tex]2(-5)^2+p(-5)-15=0[/tex]
[tex]2(25)-5p-15=0[/tex]
[tex]50-5p-15=0[/tex]
[tex]35-5p=0[/tex]
[tex]p=7[/tex]
Quadratic Equation:
[tex]2x^2+7x-15=0[/tex]
[tex]p(x^2+x)+k=0 \Rightarrow 7(x^2+x)+k=0 \Rightarrow 7x^2+7x+k=0[/tex]
[tex]\Delta=b^2-4ac[/tex]
[tex]\Delta=7^2-4(7)k[/tex]
[tex]\Delta=49-28k[/tex]
The quadratic equation having two equal roots means that the discriminant is equal to zero.
[tex]0=49-28k[/tex]
[tex]-49=-28k[/tex]
[tex]$k=\frac{49}{28} $[/tex]
[tex]$k=\frac{7}{4} $[/tex]
