Multiple choice

The remainder is 0 when x2 + kx + 9 is divided by x-1. Find roots of the given quadratic equation.

  1. 1, -9

  2. -1, 9

  3. 1,9

  4. 1, 10
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If x-1 is a factor, then f(1) = 0. 1^2 + k(1) + 9 = 0 => k = -10. Equation is x^2 - 10x + 9 = 0. Roots are (x-1)(x-9) = 0, so 1, 9.

AI explanation

By the remainder theorem, setting the divisor x - 1 to zero gives x = 1, and substituting this into the polynomial yields (1)2 + k(1) + 9 = 0, so k = -10. The quadratic equation then becomes x2 - 10x + 9 = 0. Factoring this gives (x - 1)(x - 9) = 0, meaning the roots are 1 and 9.

Keep practicing — related questions