Question

If x=2 and x=3 are roots of the equation 3x2-2ax +2b
= 0,find the value of a and b

Answer 1

If x=2 and x=3 are roots of the equation 3x2-2ax +2b

= 0,find the value of a and b

Answer 2

Given:

x = 2 and x = 3 are the roots of the equation

$3 {x}^{2} - 2ax + 2b = 0$

To find:

The value of a and b.

Solution:

The value of a and b is 15/2 and 9 respectively.

To answer this question, we will follow the following steps:

As given,

We have a quadratic equation,

$3 {x}^{2} - 2ax + 2b = 0 \: \: (i)$

Also given,

x = 2 and x = 3 are the roots of the equation.

So,

On putting x = 2 in (i), we get

$3 {(2)}^{2} - 2a(2) + 2b = 0$

$12 - 4a + 2b = 0$

$4a - 2b = 12 \: \: (ii)$

Now,

On putting x = 3 in (i), we get

$3 {(3)}^{2} - 2a(3) + 2b = 0$

$27 - 6a + 2b = 0$

$6a - 2b = 27 \: \: (iii)$

On subtracting (ii) from (iii), we get

$2a = 15$

$a = \frac{15}{2} \: or \: 7.5$

On putting the value of 'a' in (iii), we get

$2b = 45 - 27$

$2b = 18$

$b = 9$

Hence, the value of a and b is 15/2 and 9 respectively.