Multiple choice

If one root of equation $ x^2 + ax + 12 = 0 $ is 4 while the equation $x^2 + ax + b = 0 $ has equal roots, then the value of b is :

  1. $\dfrac {4}{49}$
  2. $\dfrac {49}{4}$
  3. $\dfrac {7}{4}$
  4. $\dfrac {4}{7}$
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B Correct answer
Explanation

If 4 is a root of x^2 + ax + 12 = 0, then 16 + 4a + 12 = 0, so 4a = -28, a = -7. The second equation is x^2 - 7x + b = 0. For equal roots, the discriminant must be 0: (-7)^2 - 4(1)(b) = 0, so 49 - 4b = 0, b = 49/4.

AI explanation

Since 4 is a root of x^2 + ax + 12 = 0, substituting it gives 16 + 4a + 12 = 0. Solving for a yields 4a = -28, so a = -7. The second equation x^2 + ax + b = 0 has equal roots, which means its discriminant must be zero: a^2 - 4b = 0. Substituting a = -7 gives 49 - 4b = 0, so b = 49/4.

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