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gemouljr
12.05.2021 •
Mathematics
Consider the piecewise function. The function has a discontinuity at x = 1. What are and ?
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Ответ:
Value of m must be less than![\frac{49}{12}](/tpl/images/1039/3268/73339.png)
Step-by-step explanation:
Given: Equation of curve,![y=3x^2+7x+m](/tpl/images/1039/3268/75940.png)
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,
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}](/tpl/images/1039/3268/a32e9.png)
where, a = coefficient of![x^2](/tpl/images/1039/3268/4d3aa.png)
b = coefficient of![x](/tpl/images/1039/3268/a0e3f.png)
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](/tpl/images/1039/3268/61c84.png)
⇒![\sqrt{49-12\times m}0](/tpl/images/1039/3268/450be.png)
Squaring both sides,
⇒![49-12\times m0](/tpl/images/1039/3268/2db54.png)
⇒![4912\times m](/tpl/images/1039/3268/6c87d.png)
⇒![m<\frac{49}{12}](/tpl/images/1039/3268/a1e22.png)
Therefore, Value of m must be less than![\frac{49}{12}](/tpl/images/1039/3268/73339.png)