Question

find zero of the following quadratic polynomial and verify the relationship between zero and the coefficient 3x2-27​

Answer 1

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✤ Required Answer:

✒️ GiveN:

• Polynomial P(x) = 3x² - 27

✒️ To FinD:

• Zeroes of the polynomial and checking the relationship of the zeroes with coefficients$.$

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✤ How to solve?

When α and β are the zeroes of a quadratic polynomial f(x) = ax² + bx + c, by using factor theoram (x - α) and (x - β) are the factors of f(x). So, if we will equate it we will get that a relation that is:

• α + β = -b/a = -coefficient of x/coefficient of x²
• αβ = c/a = constant term/coefficient of x²

✍️ By using this, let's solve this question....

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✤ Solution:

We have,

• f(x) = 3x² - 27

Factorising f(x),

➝ f(x) = 3(x² - 9)

➝ f(x) = 3(x + 3)(x - 3)

The zeroes are given by f(x) = 0

Now,

➝ f(x) = 0

➝ 3(x + 3)(x - 3) = 0

➝ x + 3 = 0 or x - 3 = 0

➝ x = -3 or x = 3

Hence,

• Zeroes are α = 3 and β = -3

Verifying the relation with coefficient,

• α + β = 3 + (-3) = 0
• αβ = 3(-3) = -9

According to relation,

• - coefficient of x/coefficient of x² = 0/27 = 0
• constant term/coefficient of x² = -27/3 = -9

Thus,

• Sum of zeroes = - coefficient of x/coefficient of x²
• Product of zeroes = constant term/coefficient of x²

Hence, Verified !!

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Answer 2

Answer:

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