Question

find the equation that formed by increasing each root of 2x² - 3x - 1 = by 1​

Answer 1

Given : 2x² - 3x - 1 =  = 0

To Find : equation formed by squaring each root of the equation

Solution:

2x² - 3x - 1 =  = 0

 

Let say α , β are roots of  2x² - 3x - 1 = 0

α + β =   3/2   αβ  = -1/2

Now α+1, β+1 are roots of the equation formed by   increasing each root by 1

x² - (α  + 1 +  β+ 1 )x + (α+1) (β+1)   = 0  is the Equation

α  + 1 +  β+ 1 =  α + β + 2 = 3/2  + 2 = 7/2

(α+1) (β+1) =αβ + α + β + 1 = - 1/2  + 3/2 +  1  = 2

x² - 7x/2 +2 = 0  

=> 2x² - 7x + 4 = 0

2x² - 7x + 4 = 0   is   formed by increasing each root of the equation  2x² - 3x - 1 = 0  by 1

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