Question

if √3- 1 is a solution to ax^2-5x+1=0 then, what is the value of a?

Answer 1

Answer:

$a = \frac{7\sqrt{3} -6}{4}$

Step-by-step explanation:

$f(x) = ax^{2} - 5x + 1\\f(\sqrt{3} -1) = a(\sqrt{3} -1)^{2} - 5(\sqrt{3} -1) + 1\\0 = a(3 + 1 - 2\sqrt{3} ) - 5\sqrt{3} + 5 + 1\\0 = 4a - 2\sqrt{3} a - 5\sqrt{3} + 6\\0 = 4a - 7\sqrt{3} + 6\\7\sqrt{3} - 6 = 4a\\.: a = \frac{7\sqrt{3} -6}{4}$

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