How to deal with fractional exponents.

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ibin246

28.05.2020

Mathematics

Value of m must be less than $\frac{49}{12}$

Step-by-step explanation:

Given: Equation of curve, y=3x^2+7x+m

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,

3x^2+7x+m=0

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 = $\sqrt{b^2-4ac}$

where, a = coefficient of x^2

b = coefficient of

c = constant term

⇒ a = 3, b = 7 & c = m

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

D > 0

⇒ $\sqrt{7^2-4\times3\times m}0$

⇒ $\sqrt{49-12\times m}0$

Squaring both sides,

⇒ $49-12\times m0$

⇒ $4912\times m$

⇒ $m<\frac{49}{12}$

Therefore, Value of m must be less than $\frac{49}{12}$

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