Show that 2 and – 1 3are the zeroes of the polynomial 3x³-2x²-7x-2.Also find the third zero of the polynomial About the author Evelyn
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. Reply
pls refer the attachment for your answer
the answer is -1
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.