Question

If α and β are roots of x²
-2x + 3 = 0, then equation with roots α+2, β+2 is [ ]

a) x² - 6x + 11 = 0
b) x² + 6x - 11 = 0
c) x²
-11x + 6 = 0
d) x² +11x - 6 = 0

Answer 1

optn A is correct. x^2 - 6x + 11 = 0

Answer 2

HI !!

p(x) = x² -2x + 3 

α and β are zeros of p(x)

then 

α + β = -b/a = 2
αβ = 3


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we have to find a quadratic polynomial with zeros α+2, β+2

sum of zeros = α+2 + β+2 = α +β + 4
                                          = 2 + 4
                                          = 6

product of zeros = (α+2)(β+2) = αβ + 2α +2β + 4
                                                = 3 + 2(α+β) + 4
                                                =7 + 2 × 2
                                                = 11

a quadratic polynomial is given by ,

x² - (sum of zeros ) x + (product of zeros_

x² - 6x + 11

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hence the ans is option a)