MHB How to Find Values of k for Equations with One Real Root?

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To find values of k for equations with exactly one real root, the discriminant must be set to zero using the formula b² - 4ac = 0. For the equation 3x² + (√(2k))x + 6 = 0, the discriminant involves the coefficient of x, which is √(2k). Similarly, for kx² + kx + 1 = 0, the discriminant must also equal zero to ensure a single real root. Both equations require solving for k to meet this condition. The application of the discriminant is essential for determining the values of k that yield one real root.
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Find values of k such that the equation has exactly one real root.

1. 3x^2 + (sqrt{2k})x + 6 = 0

2. kx^2 + kx + 1 = 0

Question:

Do the questions above involve the discriminant?

If so, I must apply b^2 - 4ac = 0, right?
 
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RTCNTC said:
Find values of k such that the equation has exactly one real root.

1. 3x^2 + (sqrt{2k})x + 6 = 0

2. kx^2 + kx + 1 = 0

Question:

Do the questions above involve the discriminant?

If so, I must apply b^2 - 4ac = 0, right?

Yes . you can solve with discriminant and you must apply $b^2-4ac=0$
 
Not too bad.
 
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