Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots

Mathematics

1 answer:

olga2289 [7]3 years ago

4 0

Answer:

f(x) = $3x^{3} - 6x^{2} - 15x + 30$

Step-by-step explanation:

If $\sqrt{5}$ is a root, then so is - $\sqrt{5}$

f(x) = 3(x + $\sqrt{5}$ )(x - $\sqrt{5}$ )(x - 2)

= $3(x^{2} - 5)(x - 2)$

= 3( $x^{3} - 2x^{2} - 5x + 10$ )

= $3x^{3} - 6x^{2} - 15x + 30$

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Determine the factors of x2 − 8x − 12. (x − 6)(x 2) (x 3)(x − 4) prime (x 6)(x − 2)

Ivanshal [37]

The polynomial cannot be factored in because it exists prime. Since 112 exists not a perfect square number so we cannot estimate the factors of the given equation.

<h3>What is a quadratic equation?</h3>

In a quadratic equation ax² + bx + c = 0

when (b² - 4ac) exists a perfect square only then we can factorize the equation.

In the given equation x² - 8x - 12 we have to determine the value of

b² - 4ac

From the equation, we get b = -8 and c = -12

b²- 4ac = (-8)² - 4(1)(-12)

= 64 + 48 = 112

Since 112 exists not a perfect square number so we can not estimate the factors of the given equation.

To learn more about quadratic equation refer to:

brainly.com/question/1214333

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4 0

2 years ago

Can someone help and explain this problem to me? I’m stuck

exis [7]

Answer:

c. 8 units

Step-by-step explanation:

You are to find the y-intercepts of the two functions given, then report the difference between them. The y-intercept is the y-value when x=0.

For f(x), we have ...

f(0) = 3·2^0 = 3·1 = 3

For the table, we can see that x=0 is halfway between x=-2 and x=2, so the y-intercept can be expected to be halfway between y=3 and y=-13. That value for y is ...

g(0) = (3 + (-13))/2 = -10/2 = -5

That is, the y-intercept of g(x) is -5.

The difference between f(0) and g(0) is ...

f(0) -g(0) = 3 -(-5) = 8 . . . . units