Question

Three times the square of a number when added to seven times the number result in 26.The number is?

Answer 1

2 or -
`(13)/(3)`

Explanation:

Let n be the number then three times the square of the number is 3n² and

seven times the number is 7n, thus

3n² + 7n = 26 ( subtract 26 from both sides )

3n² + 7n - 26 = 0 ← in standard form

Consider the factors of the product of the coefficient of the n² term and the constant term which sum to the coefficient of the n- term

product = 3 × - 26 = - 78 and sum = + 7

The factors are - 6 and + 13

Use these factors to split the n- term

3n² - 6n + 13n - 26 = 0 ( factor the first/second and third/fourth terms )

3n(n - 2) + 13(n - 2) = 0 ← factor out (n - 2) from each term

(n - 2)(3n + 13) = 0

Equate each factor to zero and solve for n

n - 2 = 0 ⇒ n = 2

3n + 13 = 0 ⇒ 3n = - 13 ⇒ n = -
`(13)/(3)`