Multiple choice

If 3 is one root of the quadratic equation 3x2 - px + q = 0, then find the other root, given that q - 2p = 3.

  1. 4

  2. 5

  3. 7

  4. 10

  5. Cannot say
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If 3 is a root, 3(3^2) - 3p + q = 0 => 27 - 3p + q = 0 => q - 3p = -27. We are given q - 2p = 3. Subtracting: (q - 2p) - (q - 3p) = 3 - (-27) => p = 30. Then q = 3 + 2(30) = 63. Equation: 3x^2 - 30x + 63 = 0 => x^2 - 10x + 21 = 0. Roots are 3 and 7.

AI explanation

Substitute the root x = 3 into the equation 3x2 - px + q = 0 to get 27 - 3p + q = 0, which rearranges to q = 3p - 27. Substitute this expression for q into the given equation q - 2p = 3 to get 3p - 27 - 2p = 3, yielding p = 30. Substituting p back into the equation gives q = 90 - 27 = 63, and using the product of roots formula, 3 multiplied by the second root equals q/3 = 21, so the other root is 7.

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