Question

In each of the following, determine whether the given numbers are roots of the given equations or not; 3x² – 13x – 10 = 0; 5, `(-2)/(3)`

Answer 1

3x² – 13x – 10 = 0; 5, `(-2)/(3)`
x = 5,
3(5)² - 13 x 5 - 10
= 75 - 65 - 10
= 75 - 75
= 0
∴ x = 5 is its root

if x = `(-2)/(3)`, then

`3(-2/3)^2 - 13 xx (-2)/(3) - 10`

= `(3 xx 4)/(9) + (26)/(3) - 10`

= `(4)/(3) + (26)/(3) - 10`

= `(30)/(3) - 10`

= 10 - 10
= 0

∴  x = `(-2)/(3)` is also its root.

Hence both 5, `(-2)/(3)` are its roots.