Question

the equation formed by increasing each roots of 2x2+8x+2=0 by 2is

Answer 1

Let the roots of equation be α & β

2x²-3x-1 = 0

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

If each root is increased by 2, then the new roots of the equation will be
(α+2) & (β+2)

The required equation with this roots is ;

x² - (α+2+β+2) x + (α+2)×(β+2) = 0
x² - [(3/2)+4]x + (αβ) + 2(α+β) + 4 = 0
x² -(11/2)x + (-1/2) +2(3/2)+4 = 0
x²-(11/2)x -(1/2)+7 = 0
x² - (11/2)x +(13/2) = 0

Hence the required equation will be ;
2x² - 11x +13 = 0
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