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3 years ago

What is a quartic function with only the two real zeros given?

Mathematics

1 answer:

serious [3.7K]3 years ago

4 0

Answer:

y = x^4 + 5x^3 + 5x^2 + 5x + 4

Step-by-step explanation:

Each of the latter three answers demonstrates one change of sign in its coefficients. According to Descarte's Rule of Signs, that means each of them has one positive real root. If there is a positive real root, the only two real roots will not be -4 and -1 (both negative).

The only viable option is the first one.

_____

There are other ways you can go at this. I like to let a graphing calculator show the zeros of functions of higher degree. Only the first function has only the two real roots given.

You can also evaluate each function or do synthetic division to see which polynomial has -1 or -4 as a root. Shown in the second attachment is the first function evaluated for x=-1.

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Two is a zero of the equation x^3−x^2−14x+24=0.

Keith_Richards [23]

Answer:

The factored form is equivalent to the given equation is (x - 2) (x - 3) (x + 4).

Step-by-step explanation:

Since 2 is a zero of the equation $x^{3} - x^{2} -14x + 24 = 0$

Therefore, (x - 2) is a factor of the equation $x^{3} - x^{2} -14x + 24 = 0$

Now, on dividing $x^{3} - x^{2} -14x + 24 = 0$ by (x - 2) we get,

$(x - 2) (x^{2} + x - 12)$ as shown in Fig(1)

On factorising x² + x - 12

= x² + x - 12

= x² + 4x - 3x - 12

= x (x + 4) - 3 (x + 4)

= (x - 3) (x + 4)

Now, $(x - 2) (x^{2} + x - 12)$ = $(x - 2) (x -3) (x + 4)$

So the factored form is equivalent to the given equation is (x - 2) (x - 3) (x + 4). Therefore option (c) is the correct answer.

3 0

3 years ago

If 6x = 1/126 find the value of x.

Anastasy [175]

Answer:

x = $\frac{1}{756}$

Step-by-step explanation:

Given

6x = $\frac{1}{126}$ ( divide both sides by 6 )

x = $\frac{\frac{1}{126} }{6}$ = $\frac{1}{126}$ × $\frac{1}{6}$ = $\frac{1}{126(6)}$ = $\frac{1}{756}$

6 0

3 years ago

Read 2 more answers

Which product is greater than 3 and why? GIVING BRAINLIEST

allochka39001 [22]

Answer:

D. 8/7 × 3 because the fraction is greater than 1.

I hope this helps!

7 0

3 years ago

Verify that the segment lengths form a triangle. Is the triangle acute, right, or obtuse?

Elena-2011 [213]

Answer:

The lengths do form a triangle and it is a right triangle.

Step-by-step explanation:

Part I:

To find out if 3 segment lengths form a triangle, you must verify that the sum of the two SMALLER sides (6+8) is GREATER than the longest side (10). That is true for this case. We have a triangle

Part II:

To find out the type of triangle, we must incorporate the Pythagorean theorem: