How do I factor 5x²-17x+6?

1 answer:

6 0

$5x^2-17x+6=0\ \ \ \ |write\ -17x\ as\ -15x-2x\\\\
5x^2-2x-15x+6=0\\\\\
x(5x-2)-3(5x-2)=0\\\\After\ factorization:\\ (x-3)(5x-2)=0$

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Three roots of a fifth degree polynomial function f(x) are –2, 2, and 4 i. Which statement describes the number and nature of al

bagirrra123 [75]

The correct option is f(x) has three real roots and two imaginary roots.

Given

Three roots of a fifth-degree polynomial function f(x) are –2, 2, and 4 i.

<h3>Complex conjugate</h3>

The complex conjugate of a complex number is the number with an equally real part and an imaginary part equal in magnitude but opposite in sign.

It is given that the roots of the fifth-degree polynomial function are -2, 2, and 4+i.

Since the degree of f(x) is 5, therefore there are 5 roots of the function either real or imaginary.

According to the complex conjugate root theorem, if a+ib is a root of a polynomial function f(x), then a-ib is also a root of the polynomial f(x).

Since 4+i is a root of f(x), so by complex conjugate rot theorem 4-i is also a root of f(x).

From the given data the number of real roots is 2 and the number of 2. The number of complex roots is always an even number, so the last root must be a real number.

Therefore, the correct option is f(x) has three real roots and two imaginary roots.

To know more about imaginary roots click the link given below.

brainly.com/question/1375079

3 0

1 year ago

Limitation of -4 to the left of the absolute value of x+4 divided by x+4

timama [110]

I believe you're asking about the one-sided limit,

$\displaystyle \lim_{x\to-4^-}\frac{|x+4|}{x+4}$

Recall the definition of absolute value:

• $|x| = x$ if $x\ge0$

• $|x| = -x$ if $x < 0$

Since we're approaching -4 from the left, we're effectively focusing on a domain of $x$ or $x+4$ . So, by the definition above, we have $|x+4| = -(x+4)$ . Then in the limit, we have