Respuesta :

altavistard
Think "discriminant."  There will be 2 real roots (x-intercepts) so long as the discriminant is ≥ 0.

Form the discriminant:  b^2 - 4ac becomes 7^2 - 4(3)(m).

Write and solve the inequality     49-12m≥0.

Add 12 m to both sides:               49 ≥ 12m
Divide both sides by 12:                49/12 ≥ m

So long as m is 49/12 or smaller, there will be 2 real roots.  These roots could be equal, but also could be unequal.

Answer:

Value of m must be less than  [tex]\frac{49}{12}[/tex]

Step-by-step explanation:

Given: Equation of curve, [tex]y=3x^2+7x+m[/tex]

To find: 2 x-intercepts

X-intercept of curve means zeroes of quadratic equation we get by putting y = 0.

So, The quadratic equation we get,

[tex]3x^2+7x+m=0[/tex]

Now, to have 2 x-intercept the discriminant of the quadratic equation should be greater than 0.

Therefore, By using this condition we find value of m for which given equation has 2 x-intercept.

Discriminant, D = [tex]\sqrt{b^2-4ac}[/tex]

where, a = coefficient of [tex]x^2[/tex]

            b = coefficient of [tex]x[/tex]

            c = constant term

⇒ a = 3, b = 7 & c = m

Putting these value and applying the condition of discriminant we get,

    D > 0

⇒  [tex]\sqrt{7^2-4\times3\times m}>0[/tex]

⇒  [tex]\sqrt{49-12\times m}>0[/tex]

     Squaring both sides,

⇒  [tex]49-12\times m>0[/tex]

⇒  [tex]49>12\times m[/tex]

⇒  [tex]m<\frac{49}{12}[/tex]

Therefore, Value of m must be less than  [tex]\frac{49}{12}[/tex]

Otras preguntas