Question

A and b are roots of quadratic equation the whose roots are 2a+ 3b and 3a+2b find eqn

Answer 1

Method :

    We know that if α and β be the roots of any quadratic equation, then the required quadratic equation be

    x² - (α + β) x + αβ = 0 .....(i)

Solution :

Let us take α = 2a + 3b & β = 3a + 2b

Putting these values in (i) no. eqequation, we get the required quadratic equation as

x² - (2a + 3b + 3a + 2b) x + (2a + 3b)(3a + 2b) = 0

⇒ x² - 5 (a + b) x + (6a² + 13ab + 6b²) = 0

Another Method Solution :

Since, 2a + 3b & 3a + 2b are the roots, the required quadratic equation be

{x - (2a + 3b)} {x - (3a + 2b)} = 0

⇒ x² - (3a + 2b + 2a + 3b) x + (2a + 3b) (3a + 2b) = 0

⇒ x² - 5 (a + b) x + (6a² + 13ab + 6b²) = 0

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