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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)`
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Solution
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.
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