Question

For what values of m does the graph of y = 3x2 + 7x + m have two x-intercepts?

m greater-than StartFraction 25 Over 3 EndFraction
m less-than StartFraction 25 Over 3 EndFraction
m less-than StartFraction 49 Over 12 EndFraction
m greater-than StartFraction 49 Over 12 EndFraction

Answer 1

m> -49

Explanation:

i got it right

Answer 2

m <
`(49)/(12)`

Explanation:

Using the discriminant Δ = b² - 4ac

Given a quadratic equation in standard form, y = ax² + bx + c

Then the value of the discriminant determines the nature of the roots

• For 2 real roots then b² - 4ac > 0

Given

y = 3x² + 7x + m ← in standard form

with a = 3, b = 7 and c = m, then

7² - (4 × 3 × m) > 0

49 - 12m > 0 ( subtract 49 from both sides )

- 12m > - 49

Divide both sides by - 12, reversing the symbol as a result of dividing by a negative quantity.

m <
`(49)/(12)`