Question

If -5 is a root of the quadratic equation 2x^2+px+15=0 and the equation p(x^2+x) +k=0 has equal rootsv then find p and k

Answer 1

p=13, k = 3.25

Explanation:

First, determine p:

`2x^2+px+15=0\\x=-5:\\2(-5)^2+p(-5)+15=0\\-5p+65=0\\\implies p=13`

Use this value in the second equation

`13(x^2+x)+k=0`

and write the condition for that equation having equal roots, i.e., its determinant must equal 0:

`13x^2+13x+k=0\\D=b^2-4ac=13^2-4\cdot13\cdot k=0\\52k=169\implies k = 3.25`