Question

The product of the roots of the equation ax^2+x-24=0 is equal to -2 2/5. Find the value of a in the equation.

Answer 1

a = 10

Explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 ) , then

sum of roots =
`(-b)/(a)` and product of roots =
`(c)/(a)`

given

ax² + x - 24 = 0 ← in standard form

with c = - 24 , then

`(c)/(a)` = - 2
`(2)/(5)` , so

`(-24)/(a)` = -
`(12)/(5)` ( cross- multiply )

- 12a = - 24 × 5 = - 120 ( divide both sides by - 12 )

a = 10