Verify if 1 and -3 are the zeroes of the polynomial 3x^3+5x^2-11x+3. If yes, then factorise the polynomial. Plz tell fast
Answers
Answer:
Step-by-step explanation:
Now,
p(x)=3x³+5x²-11x+3
Now,
p(1)=3(1)³+5(1)²-11(1)+3
=3+5-11+3
=0
∴1 is a factor of the polynomial
Also,
p(-3)=3(-3)³+5(-3)²-11(-3)+3
=-81+45+33+3
=0
∴ -3 is a factor of p(x)
Answer:
1,-3,1/3
Step-by-step explanation:
Given polynomial is f(x) = 3x³ + 5x² - 11x + 3.
Verification of zeroes:
When x = 1:
f(1) = 3(1)³ + 5(1)² - 11(1) + 3
= 3 + 5 - 11 + 3
= 11 - 11
= 0.
When x = 3:
f(-3) = 3(-3)³ + 5(-3)² - 11(-3) + 3
= -81 + 45 + 33 + 3
= 0.
Hence, 1 and -3 are zeroes of f(x).
Factorization of polynomial:
Given polynomial is f(x) = 3x³ + 5x² - 11x + 3
= 3x³ + 8x² - 3x² - 8x - 3x + 3
= 3x³ + 8x² - 3x - 3x² - 8x + 3
= x(3x² + 8x - 3) - 1(3x² - 8x - 3)
= (x - 1)(3x² + 8x - 3)
= (x - 1)(3x² - x + 9x - 3)
= (x - 1)(x(3x - 1) + 3(3x - 1))
= (x - 1)(x + 3)(3x - 1)
Zeroes of f(x) are given by f(x) = 0
⇒ (x - 1)(x + 3)(3x - 1) = 0
⇒ x = 1, -3, 1/3.
Therefore, the zeroes of the polynomial are 1,-3,1/3.
Hope it helps!