Question

If α+β=4 and α²+β²=40 then the formed quadratic equation having roots α and βwill be ...........................​

Answer 1

$\bigstar$ Solution :

$\bigstar$ Given :

• α+β=4 and α²+β²=40

$\bigstar$ To Find :

• quadratic equation having roots α and β

$\bigstar$ Explanation :

$\star$  α+β=4

$\star$ Squaring on both sides , we get ,

=> (α+β)² = 4²

=> α² + β² + 2αβ = 16

=> 40 + 2αβ = 46 [Given]

=> 2αβ = 6

=> αβ = 3

$\star$ So the Quadratic equation is , x² + (α+β)x + αβ = 0.

=> x² + 4x + 3 = 0 is required equation

                                                                           

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