one factor of f(c) = 5x3 + 5x2 - 170x + 280 is (x + 7). What are all the roots of the function? Use the remainder theorem
2 answers:
Answer:
Roots of the f(x) is -7 , 4 and 2.
Step-by-step explanation:
Given:
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.
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