Multiple choice

Find $m$, if the quadratic equation $(m\, -\, 1)\, x^{2}\, -\, 2\, (m\, -\, 1)\, x\, +\, 1\, =\, 0$ has real equal roots.

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For real equal roots, discriminant D = b^2 - 4ac = 0. (-2(m-1))^2 - 4(m-1)(1) = 0. 4(m-1)^2 - 4(m-1) = 0. 4(m-1)(m-1-1) = 0. 4(m-1)(m-2) = 0. m=1 or m=2. If m=1, the equation is 0=1 (not quadratic). So m=2.

AI explanation

For real and equal roots, the discriminant b squared minus 4ac must equal zero, so setting [-2(m - 1)] squared minus 4 times (m - 1) times 1 equal to 0 gives 4 times (m - 1) squared minus 4 times (m - 1) equals 0. Factoring out 4 times (m - 1) yields 4 times (m - 1) times the quantity (m - 2) equals 0. Since a quadratic equation requires m to not equal 1, m must equal 2.

Keep practicing — related questions