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Question
If -5 is a root of the quadratic equation `2x^2+px-15=0` and the quadratic equation `p(x^2+x)+k=0` 0has equal roots, find the value of k.
Solution
It is given that -5 is a root of the quadratic equation `2x^2+px-15=0`
∴ `2(-5)^2+pxx(-5)-15=0`
⇒ `-5p+35=0`
⇒` p=7`
The roots of the equation` px^2+px+k= 0=0` are equal.
∴ `D=0 `
⇒ `p^2-4pk=0`
⇒`(7)^2-4xx7xxk=0`
⇒`49-28k=0`
⇒` k=49/28=7/4`
Thus, the value of k is `7/4`
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