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Vinil7 [7]
3 years ago
8

For what values of (m) does the graph of y=mx²-5x-2 have no x-intercepts?

Mathematics
1 answer:
Natali5045456 [20]3 years ago
5 0
You need to find where the discriminant is less than zero
Remember the discriminant is b^2 - 4ac
a = m
b = -5
c = -2
Set up the inequality like this
(-5)^2 - 4m(-2) < 0
25 + 8m < 0
8m < -25
m < -25/8 < -3.125

So any number less than -3.125 will make this graph have no x-intercepts (or real roots)
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alina1380 [7]

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4 years ago
Read 2 more answers
Three roots of a fifth degree polynomial function f(x) are -2,2 and 4 + i which statement describes the number and nature of all
liubo4ka [24]

Answer:

f(x) has three real roots and two imaginary roots.

Step-by-step explanation:

Given that three roots of a fifth degree polynomial function f(x) are -2,2 and (4+i).

Now we need to find about which of the given statements describes the number and nature of all roots for this function.

We know that imaginary roots always occur in conjugate pairs.

So if (4+i) is root then (4-i) must also be the root.

So now we have total 4 roots

-2, 2, (4+i) and (4-i).

Degree of the polynomial is 5 so that means 1 root is still remaining. It can't be imaginary as that must be in pairs

So that means 5th root is real.

Hence correct choice is :

f(x) has three real roots and two imaginary roots.

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