Help!! WILL GIVE BRAINLIEST!!! What is the range of possible sizes for side x? Please explain about the rule as well.....

Mathematics

1 answer:

yaroslaw [1]3 years ago

8 0

Answer:

0.2 < x < 11.8

Step-by-step explanation:

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side, for it to form a triangle. So, we can set up 3 equations, x + 5.8 > 6, 5.8 + 6 > x, and x + 6 > 5.8. This solves out to x > 0.2, x < 11.8, and x > -0.2. We can disregard that last one, because a side can't be negative. Therefore, we know the possible range of values for x.

I hope I could be of help! Please give brainliest!

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5. f(x) = x ^ 3 + p * x ^ 2 + qx + 6 (a) Find the value of each constants p and q, given that (x - 1) is a factor of f(x) and wh

lara31 [8.8K]

Answer:

$\boxed{\textsf{ The value of p is \textbf{-2} and the value of q is \textbf{ -5}.}}$

Step-by-step explanation:

A polynomial is given to us and we need to find the value of the constants in the given equation . The given polynomial to us is :-

$\sf\implies f(x)= x^3+px^2+qx + 6$

It's mentioned that (x - 1) is a factor of f(x) . This means on putting x = 1 in the given polynomial the value of the polynomial becomes 0 .

Puttting x = 1 in f(x) :-

$\sf\implies f(x)= x^3+px^2+qx + 6 \\\\\sf\implies f(1) = 1^3 + p(1)^2+q(1) + 6 = 0 \\\\\sf\implies f(1)= 1+p + q + 6 = 0 \\\\\sf\implies \boxed{ \red{\sf p + q = -7 }}$

$\rule{200}2$

Now secondly it's given that on dividing the given polynomial by (x + 1) , the remainder is 8 . This means that on putting x = -1 the value of the given polynomial becomes 8 .

Puttting x = (-1) :-

$\sf\implies f(x)= x^3+px^2+qx + 6 \\\\\sf\implies f(-1) = (-1)^3 + p(-1)^2+q(-1)+6 = 8 \\\\\sf\implies f(-1)= -1+p -q + 6 = 8 \\\\\sf\implies p - q = 8 -6 +1 \\\\\sf\implies \boxed{ \red{\sf p - q = 3 }}$