Question

Find ^all the zeroes of the polynomial 2x cube + 3xsque
Re - 6x-3.if two of its zeroes are -√3and +√3

Answer 1

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