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3x^2+kx=-3 What is the value of K will result in exactly one solution to the equation?

User Vinzzz
by
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1 Answer

3 votes

Answer:

For k = 6 or k = -6, the equation will have exactly one solution.

Explanation:

Given a second order polynomial expressed by the following equation:


ax^(2) + bx + c, a\\eq0.

This polynomial has roots
x_(1), x_(2) such that
ax^(2) + bx + c = (x - x_(1))*(x - x_(2)), given by the following formulas:


x_(1) = (-b + √(\bigtriangleup))/(2*a)


x_(2) = (-b - √(\bigtriangleup))/(2*a)


\bigtriangleup = b^(2) - 4ac

If
\bigtriangleup = 0, the equation has only one solution.

In this problem, we have that:


3x^(2) + kx + 3 = 0

So


a = 3, b = k, c = 3


\bigtriangleup = b^(2) - 4ac


\bigtriangleup = k^(2) - 4*3*3


\bigtriangleup = k^(2) - 36

We will only have one solution if
\bigtriangleup = 0. So


\bigtriangleup = 0


k^(2) - 36 = 0


k^(2) = 36


k = \pm √(36)


k = \pm 6

For k = 6 or k = -6, the equation will have exactly one solution.

User Sardok
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7.2k points