Question

If alpha, beta be the roots of the equation 2x2

-x+3=0, form an equation

whose roots are alpha − 2, beta − 2.​

Answer 1

Step-by-step explanation:

given ; alpha = -2 , beta = -2

if alpha and beta are the roots of the given quadratic equation then the the equation is

x²-(α+β)x + αβ. = 0

x²-(-2+(-2))x + (-2)(-2) = 0

x²-(-4)x + 4. = 0

Hence ; The quadratic equation is x²+4x+4 = 0

Answer 2

Answer:

2x² + 7x + 9 = 0

Step-by-step explanation:

sum of roots = 1/2

product of roots = 3/2

∴ α + β = 1/2

αβ = 3/2

sum of roots of the required equation

= (α - 2) + (β - 2)

= (α + β) - 4

= 1/2 - 4

= -7/2

product of roots of the required equation

= (α - 2) (β - 2)

= αβ - 2(α + β) + 4

= (3/2) - 2(1/2) + 4

= 9/2

∴ Required equation:

x² - (sum of roots)x +  (product of roots) = 0

x² - (-7/2)x + (9/2) = 0

2x² + 7x + 9 = 0