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