The equation 2x2 + ax + b = 0 has only one solution. Given that a ≠ 0 and am = kb, then the relationship between k and m is
Question
The equation 2x² + ax + b = 0 has only one solution.
Given that a ≠ 0 and am = kb, then the relationship between k and m is
Solution
The equation 2x^2 + ax + b = 0 has only one solution. This means that the discriminant of the quadratic equation, which is given by a^2 - 4*b, must be equal to zero (since the discriminant gives the number of solutions of a quadratic equation).
So, we have:
a^2 - 4*b = 0
Given that a ≠ 0 and am = kb, we can substitute kb for a in the above equation:
(kb)^2 - 4b = 0 k^2 * b^2 - 4b = 0
We can factor out b:
b * (k^2 * b - 4) = 0
Since a ≠ 0, b ≠ 0. Therefore, the second factor must be zero:
k^2 * b - 4 = 0
Solving for k, we get:
k = ± sqrt(4/b)
So, the relationship between k and m is that k is equal to the positive or negative square root of 4 divided by b.
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