Solve the quadratic equation 12x^2 - 3x -9=0

B

Step-by-step explanation:

Given

12x² - 3x - 9 = 0 ( divide all terms by 3 )

4x² - x - 3 = 0

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 4 × - 3 = - 12 and sum = - 1

The factors are - 4 and + 3

Use these factors to split the x- term

4x² - 4x + 3x - 3 = 0 ( factor the fist/second and third/fourth terms )

4x(x - 1) + 3(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(4x + 3) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

4x + 3 = 0 ⇒ 4x = - 3 ⇒ x = -

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