Question

1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.


(i)
$\pi - 2\pi - 8$
​

Answer 1

Correct Question : Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. π² - 2 π - 8

Solution : p(π) = π² - 2 π - 8

• Solve this quadratic polynomial by factorisation method to find the values of zeros

→ π² - 2π - 8 = 0

→ π² - 4π + 2π - 8 = 0

→ π(π - 4) + 2(π - 4) = 0

→ (π - 4)(π + 2) = 0

Either π = 4 or π = - 2

• Verifying the relationship between the zeros and the coefficients.

Sum of zeros = -(coefficient of π)/coefficient of π² = - b/a

→ Sum of zeros = 4 + (-2) = 2/1

→ -(coefficient of π)/coefficient of π² = -(-2)/1 = 2/1

Product of zeros = Constant term/coefficient of π² = c/a

→ Product of zeros = 4 × (-2) = - 8

→ (constant term)/coefficient of π² = -8/1

•°• The relationship between the zeros and the coefficients is verified.

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Answer 2

Given :-

π² - 2π - 8

To Find :-

Find the zeroes of the following quadratic polynomials and verify the relationship

Solution :-

π² - 2π - 8

π² - (4π - 2π) - 8

π² - 4π + 2π - 8

π(π - 4) + 2(π - 4)

(π - 4)(π + 2)

Either

π - 4 = 0

π = 4

Or,

π + 2 = 0

π = -2

Sum of zeroes = -b/a

-(-2π)/π = 4 + (-2)

2π/π = 4 - 2

2/1 = 2

2 = 2

Product of zeroes = c/a

-8/1 = 4 × -2

-8 = -8

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