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statuscvo [17]
3 years ago
6

The equation x^3+x^2+ax-4=0 has one root equal to -2. Find the value of a.​

Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
5 0

Answer:

a = - 4

Step-by-step explanation:

Given x = - 2 is a root then f(- 2) = 0

f(x) = x³ + x² + ax - 4, thus

f(- 2) = (- 2)³ + (- 2)² - 2a - 4 = 0, that is

f(- 2) = - 8 + 4 - 2a - 4 = 0, thus

- 8 - 2a = 0 ( add 8 to both sides )

- 2a = 8 ( divide both sides by - 2 )

a = - 4

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3 years ago
Is x = 3 a solution of the equation 3x − 5 = 4x − 9? Explain.
Vika [28.1K]

Answer:

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Step-by-step explanation:

3(3)-5=4\\4(3)-9=3

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1 year ago
A quadratic equation is shown below:
sweet [91]

Answer:

Part A:

( 1.8333, -0.08333)

Part B:

x = 2 or x = 5/3

Step-by-step explanation:

The quadratic equation

3x^{2}-11x+10=0 has been given.

Part A:

We are required to determine the vertex. The vertex is simply the turning point of the quadratic function. We shall differentiate the given quadratic function and set the result to 0 in order to obtain the co-ordinates of its vertex.

\frac{d}{dx}(3x^{2}-11x+10)=6x-11

Setting the derivative to 0;

6x - 11 = 0

6x = 11

x = 11/6

The corresponding y value is determined by substituting x = 11/6 into the original equation;

y = 3(11/6)^2 - 11(11/6) + 10

y = -0.08333

The vertex is thus located at the point;

( 1.8333, -0.08333)

Find the attached

Part B:

We can use the quadratic formula to solve for x as follows;

The quadratic formula is given as,

x=\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}

From the quadratic equation given;

a = 3, b = -11, c = 10

We substitute these values into the above formula and simplify to determine the value of x;

x=\frac{11+/-\sqrt{11^{2}-4(3)(10) } }{2(3)}=\frac{11+/-\sqrt{1} }{6}\\\\x=\frac{11+/-1}{6}\\\\x=\frac{11+1}{6}=2\\\\x=\frac{11-1}{6}=\frac{5}{3}

6 0
3 years ago
What is 3 1/5 times 1/6?
const2013 [10]

Answer:

0.53333...

Step-by-step explanation:

8 0
2 years ago
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