Question

A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3, is
A. x² – 9
B. x² + 9
C. x² + 3
D. x² – 3

Answer 1

Answer:

[tex] x^{2}-9

Step-by-step explanation:

Sol: One zero of a polynomial is 3. Let the other zero be x.

x+ 3 = 0 x = -3.

Zeroes of the polynomial are 3and -3 Product of the zeroes = 5 x -5 = -25.

Polynomial with zeroes 3and -3 = x² - (0)x + (-9) = x² - 9

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Answer 2

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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