Multiple choice

Solve the following equation: If π‘₯ 2 βˆ’ ( π‘Ž + 1 ) π‘₯ + π‘Ž = 0 has equal roots, find the value of π‘Ž a.

  1. -1

  2. 1

  3. 5

  4. 0

  5. 3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For equal roots, the discriminant D = b^2 - 4ac = 0. Here, (a+1)^2 - 4(1)(a) = 0, so a^2 + 2a + 1 - 4a = 0, which is a^2 - 2a + 1 = 0, or (a-1)^2 = 0. Thus, a = 1.

AI explanation

For a quadratic equation to have equal roots, its discriminant (b^2 - 4ac) must be zero. Substituting the coefficients from x^2 - (a + 1)x + a = 0 gives the equation (a + 1)^2 - 4(1)(a) = 0. Expanding and simplifying this results in a^2 - 2a + 1 = 0, which factors to (a - 1)^2 = 0. Solving this gives the value of a as 1.

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