fattty wrote:

If f(x) = 3x^2 - tx + 5 is tangents to x-axis, what is the value of a positive number t?

A. 2√15

B. 4√15

C. 3√13

D. 4√13

E. 6√15

What is the meaning of this:

f(x), a quadratic in x, is tangent to x axis? It means that the graph of the quadratic touches x axis at only one point. So when y = 0, both roots are the same. So expression in x must be a perfect square when y = 0.

\(3x^2 - tx + 5 = 0\)

\((\sqrt{3}x)^2 - tx + (\sqrt{5})^2 = 0\)

To get a perfect square which looks like \(a^2 - 2ab + b^2 = (a - b)^2\), we must put \(tx = 2ab = 2*(\sqrt{3}x)*(\sqrt{5})\)

So t must be \(2*\sqrt{15}\)

Answer (A)

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