Question

Class :- 10th
Subject:- Maths
Chapter 2 :- Polynomials
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Verify that 3, –1, – (1/3) are the zeros of the cubic polynomial p(x) = 3x3 – 5x2 – 11x – 3, and then verify the relationship between the zeros and the coefficients.
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Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

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Solution :

→ p(x) = 3x³ – 5x² – 11x – 3

→ p( – 1) = 3( – 1)³ – 5( – 1)² – 11( – 1)–3

= – 3 – 5 + 11 – 3 = 0

→ p( -1/3) = 3(-1/3) -5(-1/3) - 11(-1/3)² - 11(-1/3) - 3

= (-1/9) - (5/3) + (11/3) - 3

= (-1 - 5 + 33 - 27/9)

→ p(3) = 3(3)³– 5(3)²– 11(3) – 3

= 81 – 45 – 33 – 3

= 0

Hence, we verified that 3, – 1 and -1/3 are the zeroes of the given polynomial.

Verification :

For verification, we take α = 3, β = – 1, γ = -1/3

→ α + β + γ = 3 + (-1) + (-1/3) = 5/3

= - (Coffecient of x²)/(Coefficient of y²) = -5/3

→ αβ + βγ + γα = 3•(-1) + (-1)•(-1/3) + (-1/3)•3 = (-11/3)

& αβγ = 3 × -1 × (-1/3)

= 1

→ -(Constant term)/(Coefficient term of x³)

= -(-3/3) = 1

Hence, Verefied ✓

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