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प्रश्न
If α and β are the roots of the polynomial f(x) = x2 – 2x + 3, find the polynomial whose roots are α + 2, β + 2
उत्तर
α and β are the roots of the polynomial
x2 – 2x + 3 = 0
α + β = 2; αβ = 3
Sum of the roots = α + 2 + β + 2
= α + β + 4
= 2 + 4
= 6
Product of the roots = (α + 2) (β + 2)
= αβ + 2α + 2β + 4
= αβ + 2(α + β) + 4
= 3 + 4 + 4
= 11
The quadratic polynomial
x2 – (sum of the roots) x + product of the roots = 0
x2 – (6)x + 11 = 0
x2 – 6x + 11 = 0
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