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If one root of the quadratic equation x^2-x-k=0 is the square of the other root , then k is equal to

If one root of the quadratic equation x^2-x-k=0 is the square of the other root , then k is equal to

Grade:11

3 Answers

nithin
21 Points
6 years ago
Let the rooots of the equation be a,a^2
By solving the quadratic equation a^2-a-k=0, we get a=(-1±√5/2)
We know product of the roots are c/a
So a^3=-k
K=-(-1±√5/2)^3
 
Meha
11 Points
5 years ago
Let b and b^2 be roots of the equation x^2 +x- k=0.
Sum of the roots= alpha + beta = - b/ a
-b here=-1 a=1 
So sum of the roots = b+b^2 = -1/1 = -1---------- eq n 1
Since b is the root of eq n , x^2 +x-k,
b^2 +b -k =0
b^2 + b =k --------------eq n 2 
From eqn 1 and 2  we can see that
k= -1
 
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
Dear Student,
Please find below the solution to your problem.

Let the rooots of the equation be a,a^2
By solving the quadratic equation a^2-a-k=0, we get a=(-1±√5/2)
We know product of the roots are c/a
So a^3=-k
K=-(-1±√5/2)^3

Thanks and Regards

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