Answer:
So the roots of the polynomial are -7 , 4 , 2
Step-by-step explanation:
Given the polynomial in the question
5x³ + 5x² - 170x + 280
One of the factor of this polynomial is (x + 7)
By using remainder theorem
5x²-30x+40
-----------------------------------
x+7 | 5x³ + 5x² - 170x + 280
5x³ + 35x²
----------------------------
-30x² -170x + 280
-30x² -210x
------------------
40x + 280
40x + 280
----------------
0
So the polynomial we have is
5x²- 30x + 40
divide by 5
x² - 6x + 8
(x-4)(x-2)
So the roots of the polynomial are -7 , 4 , 2
Answer:
Roots of the f(x) is -7 , 4 and 2.
Step-by-step explanation:
Given:
[tex]f(x)=5x^3 +5x^2-170x+280[/tex]
One factor of f(x) = x + 7
⇒ One root , x = -7
To find: All roots of the function Using Remainder theorem.
First we find All factors of the given f(x).
On dividing f(x) by given factor we get,
f(x) = ( x + 7 ) ( 5x² - 30x + 40 )
= ( x + 7 ) ( 5x² - 20x - 10x + 40 )
= ( x + 7 ) ( 5x( x - 4 ) - 10( x - 40 ) )
= ( x + 7 ) ( x - 4 ) ( 5x - 10 )
Remainder Theorem: Remainder theorem states that if a polynomial p(x) is divided by a linear polynomial of form x -a then remainder is given by p(a).
Put x = -7 in the given function,
f(-7) = 5(-7)³ + 5(-7)² - 170(-7) + 280 = -1715 + 245 + 1190 + 280 = 0
So, First root is -7
Now, Put x = 4
f(4) = 5(4)³ + 5(4)² - 170(4) + 280 = 320 + 80 - 680 + 280 = 0
So, Second root is 4
Now put x = 10/5 = 2
f(2) = 5(2)³ + 5(2)² - 170(2) + 280 = 40 + 20 - 340 + 280 = 0
So, Third root is 2
Therefore, Roots of the f(x) is -7 , 4 and 2.
