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One root of the quadratic equation x2 - 12x + a = 0, is thrice the other. Find the value of a?

Correct answer: B. 27

  • A. 29
  • B. 27
  • C. 28
  • D. 7

Explanation

Let the two roots be t and 3t. Their sum is t + 3t = 12, so 4t = 12 and t = 3; the roots are therefore 3 and 9, whose product is a = 3 x 9 = 27. The likely mistake is choosing a, which may come from treating the roots as 12 and 3 instead of using the given ratio.

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About Quadratic Equations

Quadratic equations contain a squared variable and can be solved by factorisation, completing the square, the quadratic formula, or graphical reasoning. Questions cover roots, the discriminant, and the relationship between roots and coefficients, while distinguishing real and repeated roots from complex or non-real roots.

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