Question

If alpha and beta are the roots of the equation 2x^2+3x+2=0,find the equation whose roots are (alpha +1)(beta+1)

Answer 1

2x^2 - 3x + 1 = 0

2x^2 - 2x - x +1 = 0

2x*(x -1) - 1*(x-1) =0

(2x-1)*(x-1) =0

alpha= 1/2 & beta = 1

2*alpha/beta = (2*1/2)/1 = 1

2*beta/alpha = 2*1/(1/2) = 4

so the equation will be

(x-1)*(x-4) = 0

x^2 - 4x -x +4 =0

x^2 - 5x +4 =0

which is the required equation

Answer 2

Answer:

Solution -

2x² - 3x + 1 = 0

2x² - 2x - x + 1 = 0

2x(x-1) - 1 (x-1) = 0

(2x -1) (x-1) = 0

Alpha = ½ & Beta = 1

2alpha /beta = 2×1(½)= 4

Hence,

The Equation will be

(x-1) (x -4) = 0

x² - 4x - x + 4 = 0

x² - 5x + 4 = 0