Question

find all zeros of the polynomial 3x³ + 10x² - 9x ‐ 4, if one of its zero is 1​

Answer 1

Answer:

We are given with one Zero of polynomial 3x³ + 10x² - 9x - 4

We are given with one Zero of polynomial 3x³ + 10x² - 9x - 4let say, p(x) = 3x³ + 10x² - 9x - 4 & zero = 1

We are given with one Zero of polynomial 3x³ + 10x² - 9x - 4let say, p(x) = 3x³ + 10x² - 9x - 4 & zero = 1Thus, one factor of p(x) = ( x - 1 )

We are given with one Zero of polynomial 3x³ + 10x² - 9x - 4let say, p(x) = 3x³ + 10x² - 9x - 4 & zero = 1Thus, one factor of p(x) = ( x - 1 )We get another factor of p(x) by dividing it with x - 1

We are given with one Zero of polynomial 3x³ + 10x² - 9x - 4let say, p(x) = 3x³ + 10x² - 9x - 4 & zero = 1Thus, one factor of p(x) = ( x - 1 )We get another factor of p(x) by dividing it with x - 1On division, quotient we get is 3x² + 13x + 4

We are given with one Zero of polynomial 3x³ + 10x² - 9x - 4let say, p(x) = 3x³ + 10x² - 9x - 4 & zero = 1Thus, one factor of p(x) = ( x - 1 )We get another factor of p(x) by dividing it with x - 1On division, quotient we get is 3x² + 13x + 4⇒ p(x) = ( x - 1 ) ( 3x² + 13x + 4 )

We are given with one Zero of polynomial 3x³ + 10x² - 9x - 4let say, p(x) = 3x³ + 10x² - 9x - 4 & zero = 1Thus, one factor of p(x) = ( x - 1 )We get another factor of p(x) by dividing it with x - 1On division, quotient we get is 3x² + 13x + 4⇒ p(x) = ( x - 1 ) ( 3x² + 13x + 4 )          = ( x - 1 ) ( 3x² + 12x + x + 4 )

We are given with one Zero of polynomial 3x³ + 10x² - 9x - 4let say, p(x) = 3x³ + 10x² - 9x - 4 & zero = 1Thus, one factor of p(x) = ( x - 1 )We get another factor of p(x) by dividing it with x - 1On 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) ]

We are given with one Zero of polynomial 3x³ + 10x² - 9x - 4let say, p(x) = 3x³ + 10x² - 9x - 4 & zero = 1Thus, one factor of p(x) = ( x - 1 )We get another factor of p(x) by dividing it with x - 1On 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 )

We are given with one Zero of polynomial 3x³ + 10x² - 9x - 4let say, p(x) = 3x³ + 10x² - 9x - 4 & zero = 1Thus, one factor of p(x) = ( x - 1 )We get another factor of p(x) by dividing it with x - 1On 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

We are given with one Zero of polynomial 3x³ + 10x² - 9x - 4let say, p(x) = 3x³ + 10x² - 9x - 4 & zero = 1Thus, one factor of p(x) = ( x - 1 )We get another factor of p(x) by dividing it with x - 1On 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

We are given with one Zero of polynomial 3x³ + 10x² - 9x - 4let say, p(x) = 3x³ + 10x² - 9x - 4 & zero = 1Thus, one factor of p(x) = ( x - 1 )We get another factor of p(x) by dividing it with x - 1On 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 ) = 0x + 4 = 0   & 3x + 1 = 0

We are given with one Zero of polynomial 3x³ + 10x² - 9x - 4let say, p(x) = 3x³ + 10x² - 9x - 4 & zero = 1Thus, one factor of p(x) = ( x - 1 )We get another factor of p(x) by dividing it with x - 1On 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 ) = 0x + 4 = 0   & 3x + 1 = 0x = -4   &  x = -1/4

We are given with one Zero of polynomial 3x³ + 10x² - 9x - 4let say, p(x) = 3x³ + 10x² - 9x - 4 & zero = 1Thus, one factor of p(x) = ( x - 1 )We get another factor of p(x) by dividing it with x - 1On 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 ) = 0x + 4 = 0   & 3x + 1 = 0x = -4   &  x = -1/4Therefore, All zeroes are 1 , -4 & -1/4

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