Find the quadratic polynomial whose one zero is 3 - √3 and product of zeroes is 4.
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Find the quadratic polynomial whose one zero is 3 - √3 and product of zeroes is 4.
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Answer:
1÷3-√3((3-√3)x²-10x+4(3-√3))
Step-by-step explanation:
let roots be A and B
A=3-√3
Now, AB=4
B=4\(3-√3)
Now, A +B = 10\(3-√3)
Polynomial= x²-(A+B)x+AB
Put the value and find the lcm .
Sum of Zeroes = 3 - √3
Product of Zeroes = 4
If one Zero is 3 - √3, then other must be 3 + √3.
Sum of Zeroes = (3 - √3 + 3 + √3) = 6
Product of Zeroes = 4
We Know that the Formula to find Quadratic Equation f(x) is
f(x) = K[x² - (α + β)x + α.β]
= K[x² - 6x + 4]
= K[x² - 6x + 4]
= x² - 6x + 4 [ ∵ K is a Constant]
The quadratic equation is x² - 6x + 4.