Verified Solution • 2025–26 Session moderate

QJEEM21Ma3b6d: JEE Main 2021 Mathematics - Class 12 JEEM21Ma3b6d Solution: The coefficients a, b and c of the quadratic equation, ax 2 +…

The coefficients a, b and c of the quadratic equation, ax2 + bx + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is :

Multiple Choice Options

  • A 172{1 \over {72}}
  • B 5216{5 \over {216}}
  • C 136{1 \over {36}}
  • D 154{1 \over {54}}

Step-by-Step Verified Solution

ax2 + bx + c = 0

a, b, c ∈\in {1,2,3,4,5,6}

n(s) = 6 × 6 × 6 = 216

For equal roots, D = 0 ⇒\Rightarrow b2 = 4ac

⇒\Rightarrow ac = b24{{{b^2}} \over 4}

Favourable case :

If b = 2, ac = 1 ⇒\Rightarrow a = 1, c = 1

If b = 4, ac = 4 :
a = 1, c = 4
a = 4, c = 1
a = 2, c = 2

If b = 6, ac = 9 ⇒\Rightarrow a = 3, c = 3

∴\therefore Favorable cases = 5

∴\therefore Required probability = 5216{5 \over {216}}

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