if -5 is a root of the quadratic equation 2s^2+ps-15=0 and quadratic equation p(s^2+s)+k=0 has equal roots find the value of k
Answers
Step-by-step explanation:
Given:-
-5 is a root of the quadratic equation 2s^2+ps-15=0 and quadratic equation p(s^2+s)+k=0 has equal roots
To find:-
find the value of k ?
Solution:-
Given quadratic equation is 2s^2 +ps -15 = 0
If -5 is a root of the given equation then
it satisfies the given equation
Put s = -5 then
=>2(-5)^2+p(-5) -15 = 0
=>2(25)-5p-15 = 0
=>50-5p-15 = 0
=>35-5p = 0
=>35 = 5p
=>5p = 35
=>p = 35/5
=>p = 7
The value of p = 7
given another equation is p(s^2+s)+k=0
On Substituting the value of p in the equation
=>7(s^2+s)+k = 0
=>7s^2+7s +k = 0
On comparing with the standard quadratic equation ax^2+bx+c = 0 then
a = 7
b=7
c = k
Given that it has equal roots
we know that
The quadratic equation ax^2+bx+c = 0 has equal roots then it's discriminant must be zero.
=>b^2-4ac = 0
=>7^2-4(7)(k) = 0
=>49-28k = 0
=>28k = 49
=>k = 49/28
=>k = 7/4
Therefore,k = 7/4
Answer:-
The value of k for the given problem is 7/4
Used formulae:-
- .The quadratic equation ax^2+bx+c = 0 has equal roots then it's discriminant must be zero.