Question

Find the number of integral values of x such that (x-10)(x-20)(x-30)(x-40)<0​

Answer 1

Answer:

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Answer 2

Answer:

Number of integral values = 18

Step-by-step explanation:

• The given polynomial is : (x-10)(x-20)(x-30)(x-40)<0​

       The left hand side should be negative. To get the negative value we can expand it like this:

(i) When the value of x < 10: x - 10 = -ve, x - 20 = -ve, x - 30 = -ve and           x - 40 = -ve.

The multiplication of 4 negative values will give a positive value, so x can not be less than 10.

(ii) When  10 < x < 20: x - 10 = +ve,   x - 20 = -ve,     x - 30 = -ve   and           x - 40 = -ve.

The multiplication of 3 negative values will give a negative value. So this condition is satisfied and x is an integer. The possible values of x are = 11, 12, 13, 14, 15, 16, 17, 18, 19.

(iii) When the value of 20 < x < 30: x - 10 = +ve, x - 20 = +ve, x - 30 = -ve and   x - 40 = -ve.

The multiplication of 2 negative values will give a positive value, so this condition will not be satisfied.

(iv) When the value of 30 < x < 40: x - 10 = +ve, x - 20 = +ve, x - 30 = +ve and   x - 40 = -ve.

The left hand side will be negative. So this condition is satisfied and x is an integer. The possible values of x are = 31, 32, 33, 34, 35, 36, 37, 38, 39.

• Conclusion: In 10 < x < 20 this range there are 9 values of x and in 30 < x < 40 this range there are 9 values of x.

        Number of integral values = 9 + 9 = 18

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