Question

For what values of m dose the graph of y=3x^2+7x+m have two x-intercepts?

Answer 1

Answer:

$\large\boxed{m$

Step-by-step explanation:

x-intercepts are for y = 0.

Put y = 0 to the equation y = 3x² + 7x + m.

3x² + 7x + m = 0

Calculate the discriminant of quadratic equation ax² + bx + c = 0:

Δ = b² - 4ac

if Δ < 0, then an equation has no solution

if Δ = 0, then an equation has one solution

if Δ > 0, then an equation has two solution.

3x² + 7x + m = 0

a = 3, b = 7, c = m

Δ = 7² - 4(3)(m) = 49 - 12m

Two x-intercepts for Δ > 0.

Solve the inequality:

$49-12m>0$           subtract 49 from both sides

$-12m>-49$          change the signs

$12m$          divide both sides by 12

$m$