1313Ques16.the 3rd zeroes of the polynomial.Show that 2 and are the ze

1.	1313Ques16.the 3rd zeroes of the polynomial.Show that 2 and are the zeroes of the polynomial 3x3-2x2-7x-2. Also, find
Answer» 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 Let third zero be p, then => 2 -1/3 + p = 2/3=> p = -1 Thus, -1 is the third zero of the polynomial.

1313Ques16.the 3rd zeroes of the polynomial.Show that 2 and are the zeroes of the polynomial 3x3-2x2-7x-2. Also, find

Answer»

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

Let third zero be p, then => 2 -1/3 + p = 2/3=> p = -1

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