Question

Find the number of divisors of 3780 excluding 1 and the no itself?
WA
Select one:
O a. 45
O b. 40
O C. 48
O d. 36
If one of the roots of the quadratic equation x^2+mx+24=0 is 1.5, then what​

Answer 1

Given :  3780

To Find : number of divisors of 3780 excluding 1 and the no itself

O a. 45

O b. 40

O C. 48

O d. 46

Solution:

    3780

2   1890

2     945

3     315

3      105

3      35

5      7

7       1

3780 = 2 x 2 x 3 x 3 x 3 x 5 x 7

=> 3780 = 2² x 3³ x 5¹ x 7¹

(2 + 1)(3 + 1)(1  + 1)(1 + 1)

= 3 x 4 x 2 x 2

= 48

Total Divisors = 48

Exclude 1 and number itself

Divisors = 48 - 2 = 46

x² + mx + 24 = 0

one root = 1.5 so other roots = 24/1.5 = 16

m = - (16 + 1.5) = -17.5

divisors excluding 1 and itself are 2,3,4,5,6,7,9,10,12,14,15,18,20,21,

27,28,30,35,36,42,45,54,60,63,70,84,90,105,108,126,135,140,180,189,210,

252,270,315,378,420,540,630,756,945,1260,1890.

Therefore, there are 46 divisors of 3780 excluding 1 and itself.

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