Multiple choice

If one root of the equation $ax^{2} + x - 3 = 0$ is $-1$, then what is the other root?

  1. $\dfrac {1}{4}$
  2. $\dfrac {1}{2}$
  3. $\dfrac {3}{4}$
  4. $1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If -1 is a root, then a(-1)^2 + (-1) - 3 = 0, so a - 4 = 0, a = 4. The equation is 4x^2 + x - 3 = 0. Factoring: (4x - 3)(x + 1) = 0. The roots are -1 and 3/4.

AI explanation

Substitute x equals minus 1 into the equation ax squared plus x minus 3 equals 0 to get a times 1 minus 1 minus 3 equals 0, which solves to a equals 4. The equation is now 4x squared plus x minus 3 equals 0, and the product of its roots equals the constant term divided by the leading coefficient, which is minus 3 divided by 4. Since one root is minus 1, multiplying it by the other root gives minus 3 divided by 4; therefore, the other root is 3 divided by 4.

Keep practicing — related questions