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 :
Solution
ax<sup>2</sup> + bx + c = 0
<br><br>a, b, c $\in$ {1,2,3,4,5,6}
<br><br>n(s) = 6 × 6 × 6 = 216
<br><br>For equal roots, D = 0 $\Rightarrow$ b<sup>2</sup> = 4ac
<br><br>$\Rightarrow$ ac = ${{{b^2}} \over 4}$
<br><br>Favourable case :
<br><br>If b = 2, ac = 1 $\Rightarrow$ a = 1, c = 1
<br><br>If b = 4, ac = 4 :
<br>a = 1, c = 4
<br>a = 4, c = 1
<br>a = 2, c = 2
<br><br>If b = 6, ac = 9 $\Rightarrow$ a = 3, c = 3
<br><br>$\therefore$ Favorable cases = 5
<br><br>$\therefore$ Required probability = ${5 \over {216}}$
About this question
Subject: Mathematics · Chapter: Probability · Topic: Classical and Axiomatic Probability
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