Question

Find the zeroes of each of the following quadratic polynomials and verify the relationship between the zeroes and their coefficient 3x^2-2x-1.​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Given:-

• P(x) => 3x² - 2x - 1

To find:

• Zeroes of the polynomial.
• Relationship between the zeroes and co - efficients.

Solutions:-

P(x) => 3x² - 2x - 1

=> 3x² - 2x - 1

=> 3x² - 3x + x - 1

=> 3x(x - 1) + 1(x - 1)

=> (3x + 1) (x - 1)

=> x = -1/3 Or x = 1

Hence, x = -1/3 Or x = 1

Verification:-

P(x) => 3x² - 2x - 1

• a = 3
• b = -2
• c = -1

Let α and β are the zeroes of the given polynomial.

• α = -1/3
• β = 1

Sum of zeroes = -b/a

=> -1/3 + 1 = -(-2)/3

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

=> 2/3 = 2/3

Product of zeroes = c/a

=> -1/3 × 1 = -1/3

=> -1/3 = -1/3

Verify