Question

If the roots of the equation 2x²-5x+b=0 are in the ratio of 2:3 then find the value of b ?

Answer 1

Answer:

3

Step-by-step explanation:

Let α  and β be the roots of the equation.

α : β = 2:3 => α/β = 2/3 => α = 2/3 * β.

Sum of roots = α + β = -b/a = -5/2

Product of roots = αβ = c/a = b/2

Substitute value of α in first equation.

α + β = -5/2

2β/3 + β = -5/2

5β/3 = - 5/2

β = -3/2, α = -1

//Now substitute α and β values in 2nd equation.

αβ = b/2

(-3/2)(-1)  = b/2

=> b/2 = 3/2

=> b = 3