Question

find quadratic polynomial whose zeros are 3+✓5and 3-✓5​

Answer 1

Answer:

p(x) = x² - 6x + 4

Step-by-step explanation:

Quadratic polynomial can be written as,

p(x) = x²-(A+B)x+ ABx

where A and B are zeros of p(x).

Here, A=3+√5 , B = 3-√5

p(x) = x² -(3+√5+3-√5)x + (3+√5)(3-√5)

p(x) = x² - 6x + (9-5)

p(x) = x² - 6x + 4

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Answer 2

Answer:

x²− 6x + 4

Step-by-step explanation:

Let α = 3 + √5 and β = 3√5

Sum of zeros = α + β = 3 + √5 + 3 − 5 = 6

Product of zeros = αβ = (3 + √5)(3 − √5) = 9 − 5 = 4

Also, Sum of roots = -b = -6

a 1

Product of roots = c = 4

a 1

⟹a = 1, b = −6 and c = 4

Hence, the quadratic polynomial is x²− 6x + 4