Question

Show that 2 and -  1/3are the zeroes of the polynomial 3x³-2x²-7x-2.Also find the third zero of the polynomial​

Answer 1

Answer:

Let α,0,0 be the zeros of ax3+bx2+cx+d. Then, sum of zeros = -ba⇒α+0+0=-ba⇒α=-ba. Hence, the third zeros is -ba.

Hope this hint is very useful for you .

Answer 2

-1

Given polynomial is f(x) = 3x³ - 2x² - 7x - 2

Consider f(2) = 3.(2)³ - 2(2)² - 7(2) - 2

= 3.8 - 8 - 14 - 2

= 0

Hence , 2 is the zero of the polynomial.

Consider f(-1/3)

= 3.(-1/3)³ - 2(-1/3)² - 7(-1/3) - 2

= -3/27 - 2/9 + 7/3 - 2

= -1/9 - 2/9 + 7/3 - 2

= -3/9 +7/3 - 2

= 2 - 2 = 0

Hence, -1/3 is the zerof of f(x).

We Know Sum of zeros of f(x) is -ve of coefficient of x²/Coefficient of x³

=> 2 -1/3 + p = 2/3

=> p = -1

Thus, -1 is the third zero of the polynomial.

Hope, it helped !