Mathematics Test 10

Result

Mathematics Test 10

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
4 / -1

How many real solutions does the equation x⁷ + 14x⁵ + 16x³ + 30x – 560 = 0 have?

A
3

B
5

C
7

D
1

Solution

f(x) = x⁷ + 14x⁵ + 16x³ + 30x - 560

f′(x) = 7x⁶ + 70x⁴ + 48x² + 30 > 0. Since f(x) is odd degree polynomial and is increasing.

⇒ f(x) has exactly one solution.
Question 2
4 / -1

A person throws two dice, one the common cube and the other a regular tetrahedron, the number on the lowest face being taken in the case of the tetrahedron. What is the chance that the sum of the numbers thrown is not less than 5 ?

A
1/4

B
3/4

C
3/16

D
3/8