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Cerrena [4.2K]
2 years ago
13

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

Mathematics
1 answer:
Scorpion4ik [409]2 years ago
3 0

Answer:

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

Step-by-step explanation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

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} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\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 \sqrt{36}

k = \pm 6

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

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The formula for finding the perimeter of a quadrilateral is  Length + Length + Width + Width.

<h3>What is Perimeter?</h3>
  • A perimeter is the path that surrounds a certain shape. To calculate the path that surrounds a quadrilateral, we need to get the sum of its four sides, both lengths and widths, lengths being the longest sides and the widths being the shortest.
  • The formula used for calculating perimeter is Perimeter = Length + Length + Width + Width.
  • For instance, to calculate the perimeter of a parallelogram with a side of 5 cm and one of 3 cm, we insert the numbers in their corresponding spot in the formula as such: Perimeter=5+5+3+3=16 cm or since parallelograms have 2 sets of 2 equal sides, we can use this formula Perimeter=(5×2)+(3×2)=10+6=16 cm.
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Learn more about quadrilateral here:

brainly.com/question/23935806

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