Question

The product of the roots of the equation : 1/2 x 2 - 5/4 x - 3=0

Answer 1

Explanation:

(X-4)(2x+3)=0

X-4=0 2x+3=0

X=4 X=-3/2

Answer 2

Product of the roots of the equation
`\bold{(1)/(2) x^(2)-(5)/(4) x-3=0}` is -6

Solution:

If
`\alpha` and
`\beta` are the roots of any quadratic equation
`x^(2)+b x+c=0` then,

Sum of roots
`\alpha+\beta=-(b)/(a)`

Product of roots
`\alpha * \beta` =
`(c)/(a)`

Given that

`(1)/(2) x^(2)-(5)/(4) x-3=0`

On simplifying the above equation,

`(2 x^(2)-5 x-12)/(4)=0`

`2 x^(2)-5 x-12=0`

Here a = 2, b = -5 and c = -12

So product of roots is
`(c)/(a)` that is
`(-12)/(2) = -6`

Hence product of the roots of the equation
`(1)/(2) x^(2)-(5)/(4) x-3=0` is -6