Multiple choice

If quadratic equation $\displaystyle 6x^{2}-7x+2=0$ has one root $\displaystyle \frac{1}{2}$ then the second root will be--

  1. $\displaystyle -\frac{1}{2}$
  2. $\displaystyle \frac{2}{3}$
  3. $\displaystyle \frac{3}{2}$

  4. 1
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B Correct answer
Explanation

For a quadratic equation ax^2 + bx + c = 0, the product of roots is c/a. Here, (1/2) * r2 = 2/6 = 1/3. Therefore, r2 = (1/3) * 2 = 2/3.

AI explanation

We use the relationship between the coefficients and roots of a quadratic equation, which states that the product of the roots equals c/a. For 6x^2 - 7x + 2 = 0, the product of the roots is 2/6. Multiplying this product of 1/3 by the given first root of 1/2 gives the second root as 2/3.

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