if alpha and beta are the roots of the equation 2 x square - 7 x - 3 is equal to 0 find alpha + beta

Values for alpha and beta are 0.5 and 3.

Step-by-step explanation:

2x² - 7x - 3 = 0

2x² - 7x - 3 = (2x - 1 )(x - 3)

∴ (2x - 1 )(x - 3) = 0

The only way to get zero by multiplying two values together, is if one of those values is qual to zero. Therefore, either (2x - 1 )=0, or (x - 3)=0.

If (2x - 1 )=0

∴2x=1

∴x=0.5

If (x - 3)=0

∴x=3

We have two values for x. These values represent alpha and beta.

(BTW - I'm not sure from the phrasing of your question whether or not you just want to find the values or whether you want to find the sum of the values (I don't know if you used '+' to mean 'and' or 'plus'), but if you do want to find the sum, it's of course just 0.5+3= 3.5.)

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

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