Question

One root of the quadratic equation 8x² + mx + 15 = 0 is `3/4`. Find the value of m. Also, find the other root of the equation.

Answer 1

Given quadratic equation is 8x² + mx + 15 = 0   ...(i) 

One of the roots of (i) is `3/4` so it satisfies (i)

`=> 8(3/4)^2 + m(3/4) + 15 = 0`

`=> 9/2 + (3m)/4 + 15 = 0`

`=> 18 + 3m + 60 = 0`

`=> 3m + 78 = 0`

`=> 3m = -78`

`=> m = -78/3`

`=> m = -26`

So, the equation (i) becomes 8x² – 26x + 15 = 0

`=> 8x^2 - 20x - 6x + 15 = 0`

`=> 4x(2x - 5) - 3(2x - 5) = 0`

`=> (4x - 3) (2x - 5) = 0` 

`=> (4x - 3) = 0` or `(2x - 5) = 0`

`=> x = 3/4` or `x = 5/2`

`=> x = 3/4, 5/2`

Hence, the other root is `5/2`