Find all zeros of the polynomial 3x³+10x²-9x-4. If one its zero is 1
Answers
Answer:
All zeroes are 1 , -4 & -1/4
Step-by-step explanation:
We are given with one Zero of polynomial 3x³ + 10x² - 9x - 4
let say, p(x) = 3x³ + 10x² - 9x - 4 & zero = 1
Thus, one factor of p(x) = ( x - 1 )
We get another factor of p(x) by dividing it with x - 1
On division, quotient we get is 3x² + 13x + 4
⇒ p(x) = ( x - 1 ) ( 3x² + 13x + 4 )
= ( x - 1 ) ( 3x² + 12x + x + 4 )
= ( x - 1 ) [ 3x(x + 4) + (x + 4) ]
= ( x - 1 ) ( x + 4 ) ( 3x + 1 )
For zeroes put p(x) = 0
⇒ ( x - 1 ) ( x + 4 ) ( 3x + 1 ) = 0
x + 4 = 0 & 3x + 1 = 0
x = -4 & x = -1/4
Therefore, All zeroes are 1 , -4 & -1/4
Answer:
Step-by-step explanation:
p(x) = 3x³ + 10x² - 9x - 4 & zero = 1
Thus, one factor of p(x) = ( x - 1 )
We get another factor of p(x) by dividing it with x - 1
On division, quotient we get is 3x² + 13x + 4
⇒ p(x) = ( x - 1 ) ( 3x² + 13x + 4 )
= ( x - 1 ) ( 3x² + 12x + x + 4 )
= ( x - 1 ) [ 3x(x + 4) + (x + 4) ]
= ( x - 1 ) ( x + 4 ) ( 3x + 1 )
For zeroes put p(x) = 0
( x - 1 ) ( x + 4 ) ( 3x + 1 ) = 0
x + 4 = 0 & 3x + 1 = 0
x = -4 & x = -1/4
Therefore, All zeroes are 1 , -4 & -1/4