Question

If alpha and beta are the roots of equation x^2+3x+3=0, then the equation of whose roots are alpha+1/beta and beta+1/alpha?

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Answer 1

Step-by-step explanation:

Given Equation: x² - 2x + 3 = 0

Sum of roots = a + B = -b/a = -(-2)/1 = 2

→ Sum of roots of new equation = a + 2 +

B+2

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=a+ß +

→ Sum of roots of new equation =

4

→ Sum of roots of new equation = 2 + 4

= 6

Similarly, Product of roots = c/a = aß = 3/1 = 3

Product of roots of new equation = (a +

2)(B+2)

→ Product of roots of new equation = aß

+ 2a + 2B + 4

→ Product of roots of new equation = aß

+2(a+B) + 4

→ Product of roots of new equation = 3 +

2 (2) + 4

→ Product of roots of new equation = 3

→ Product of roots of new equation = aß

+ 2(a+B) + 4

→ Product of roots of new equation = 3 +

2(2)+4

→ Product of roots of new equation = 3

+ 4 + 4 = 11

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Therefore new equation is given as: → x² - (Sum of roots ) x + Product of

roots

⇒ x² - 6x + 11 = 0: Required Equation