Given that the equation $k^2 + 12x + k = 0$, where $k$ is a positive constant, has equal roots, find the value of $k$. - Edexcel - A-Level Maths Pure - Question 5 - 2005 - Paper 2
Question 5
Given that the equation $k^2 + 12x + k = 0$, where $k$ is a positive constant, has equal roots, find the value of $k$.
Worked Solution & Example Answer:Given that the equation $k^2 + 12x + k = 0$, where $k$ is a positive constant, has equal roots, find the value of $k$. - Edexcel - A-Level Maths Pure - Question 5 - 2005 - Paper 2
Step 1
Attempt to use discriminant $b^2 - 4ac$
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Answer
To determine the condition for the quadratic equation to have equal roots, we use the discriminant formula:
b2−4ac=0.
In our equation, we identify:
Coefficient of x2 (a) = k
Coefficient of x (b) = 12
Constant term (c) = k.
Substituting these values into the discriminant gives:
122−4(k)(k)=0.
This simplifies to:
144−4k2=0.
Step 2
Attempt to solve for $k$
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Answer
Rearranging the equation gives:
4k2=144.
Dividing both sides by 4, we find:
k2=36.
Taking the positive square root (since k is a positive constant) leads to:
