Question

a quadratic polynomil,sum of whose zeros is o and one zero is 3 is...​

Answer 1

Answer: The correct option is (a) : x² - 9

Let α  and β are the zeroes of the  polynomial .

Given : Sum of the zeroes (α + β) = 0 and one zero (α) = 3 .

(α + β) = 0 ………………..(1)

3 + β = 0

β = 0 - 3

β = - 3

On substituting β = - 3 in eq 1 .

(α + β) = 0

α +(-3 )= 0

α - 3 = 0

α = 3  

Product of the zeroes = αβ

Product of the zeroes = 3 × -3 = -9

αβ = - 9 ………………(2)

Then, the required quadratic polynomial is :  

[x² –(sum of the zeroes)x + (product of the zeroes)] = 0  

= [x² –(α + β)x + (α β)]  

= x² -(0)x + (-9)

[From eq 1 & 2 ]

= x² - 9

Hence, the required quadratic polynomial is x² - 9.

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Answer 2

Answer:

Let the zeroes be α and β

Here, Sum of zeroes = 0

α + β = 0

3 + β = 0 [∵ α = 3]

β = -3

We know that,

α + β = -b/a and α × β = c/a

⇒ 0 = -b/a and -9 = c/a

∴ a = 1, b = 0 and c = -9

General form of quadratic polynomial = ax² + bx + c

So, the required polynomial = x² - 9

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Step-by-step explanation: