IPMAT Indore 2024 (MCQ) - The number of real solutions of the equation x^2 - 10|x| - 56 = 0 is | PYQs + Solutions | AfterBoards
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Algebra
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Modulus

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The number of real solutions of the equation x2−10∣x∣−56=0x^2 - 10|x| - 56 = 0 is

Correct Option: 4
There are two cases when we open the modulus:
I. Positive Sign (assumption: x>0x>0)
x2−10∣x∣−56=0x^2 - 10|x| - 56 = 0 \newline x2−10x−56=0x^2 - 10x - 56 = 0 \newline x=14,−4x = 14, -4
Note: Become smart in finding the values of xx without writing all the steps (you find the two numbers to split the middle term, reverse the signs).
Since our assumption was x>0x>0, then only x=14x=14 is the accepted value.
II. Negative Sign (assumption: x<0x<0)
x2−10∣x∣−56=0x^2 - 10|x| - 56 = 0 \newline x2+10x−56=0x^2 + 10x - 56 = 0 \newline x=−14,4x = -14, 4
Since our assumption was x<0x<0, then only x=−14x=-14 is the accepted value.
Thus, there are only 2 solutions.
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