Question

12. Form a quadratic polynomial
whose one zero is 2+v3 and product
of zeros is 1,
O (A). x2+4x-1
O (B). X2-4x-1
O (C). X2+4x+1
O (D). X2-4x+1​

Answer 1

Answer:

ax^2+bx+c=k (x^2-(Alpha + beta)+alphabeta

Where alpha and beta are roots

Given-

Alpha+ beta= 2+ root 3

alpha × beta=1

=k (x^2-x (2+ root 3)+1

=k (x^2-2x root 3 x +1)

so the polynomial is x^2-x (2 + root 3)+1

Option D is correct

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Answer 2

$\large\bf\underline{Given:-}$

• One zero of required polynomial is 2+√3
• product of zeroes = 1

$\large\bf\underline {To \: find:-}$

• Quadratic polynomial

$\huge\bf\underline{Solution:-}$

Given zero = 2+√3 then the other zero is 2-√3

Let α and β are the zeroes of the required polynomial.

• α = 2 + √3
• β = 2 - √3

α + β = 2 +√3 + 2-√3

➝ α + β = 4

• αβ = 1

Formula for quadratic polynomial :-

$\bf \: {x}^{2} - ( \alpha + \beta )x + \alpha \beta$

➝ x² - (4)x + 1

➝ x² - 4x + 1

So, the required polynomial is x² - 4x + 1

Option d is correct

$\large\underline{\bf\: Verification:-}$

p(x) = x² - 4x + 1

• a = 1
• b = - 4
• c = 1

Sum of zeroes = -b/a

➝ 4 = -(-4)/1

➝ 4 = 4

Product of zeroes = c/a

➝ 1 = 1/1

➝ 1 = 1

LHS = RHS

hence Verified