Use the function f(x) = -3x^2+13x+3 to find x when f(x) = -7
2 answers:
Answer:
x = 5 or x = -
Step-by-step explanation:
given f(x) = - 7, then
- 3x² + 13x + 3 = - 7 ( add 7 to both sides )
- 3x² + 13x + 10 = 0 ← in standard form
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x term
product = - 3 × 10 = - 30 and sum = + 13
The factors are + 15 and - 2
Use these factors to split the middle term
- 3x² + 15x - 2x + 10 = 0 ( factor by grouping the 1/2 and 3/4 terms )
- 3x(x - 5 ) - 2(x - 5 ) = 0 ( factor out (x - 5 ) )
(x - 5)(- 3x - 2) = 0
equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
- 3x - 2 = 0 ⇒ - 3x = 2 ⇒ x = -
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