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Question

# If the square of a number is 80 less than 18 times the number, then the number can be .

A
-8 or -10
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B
-8 or 10
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C
8 or -10
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D
8 or 10
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Solution

## The correct option is D 8 or 10Let the number be x. Square of the number = x2 Given, the square of the number is 80 less than 18 times the number ⇒ x2 = 18x -80 ⇒ x2 - 18x +80 = 0 The roots of a quadratic equation ax2+bx+c=0 is given by x=−b ± √b2−4ac2a. Hence, the roots are x=18 ± √(−18)2−4× 1× 802× 1 x=18 ± √324−(4×80)2 x=18 ± √42 x=18 ± 22 x=8 or 10

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