Question

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

Answer 1

Solving Question:

We are given the ratio of zeros .So we can take the common factor as 'k' thus, the zeros are 2k and 3k .Then to find the value of 'k' .Then trough the equations below we can find the  answer

If α and β are the zeros then,

α + β = -b/a

α * β = c/a

Solution:

zeros are 2k and 3k

α + β = -b/a

⇒ 2k +3k = -(-5)/2 [polynomial = 2x^2 - 5x + b = 0 , and a = 2 , b = -5 , c =b]

or, 5k = 5/2

or, k = 1/2

Then the zeros are ,

2k = 2 *(1/2) = 1

and,

3k = 3*(1/2) = 3/2

α = 1 , β = 3/2

To find the value of 'b'

α * β = c/a

⇒ α * β = b/a [polynomial = 2x^2 - 5x + b = 0 , and a = 2 , b = -5 , c =b]

or,  α * β =  b/2

substitute values ,

1(3/2) = b/a

or,  3/2 = b/a

⇒ b = 3

∴ The value of 'b' is 3

Answer 2

$value \: of \: b \: is \: 3 \\ \\ i \: hope \: this \: will \: help \: you \:$