Multiple choice

For the quadratic equation $ax^2 + bx + c = 0, a, b, c, \in Q$, If $D = 0$ then ................... Choose the correct option in respect to the statements below. (P) The roots of the equation are equal. (Q) The roots of the equation are not equal. (R) The roots of the equation are rational numbers. (S) The roots of the equation has no roots.

  1. Statements $P$ and $R$ are correct
  2. Statements $Q$ and $R$ are correct
  3. Only statement $S$ is correct
  4. Only statement $P$ is correct
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A Correct answer
Explanation

For a quadratic equation with rational coefficients, if the discriminant D is equal to 0, then the roots are real, rational, and equal. Therefore, statements P (roots are equal) and R (roots are rational numbers) are correct.

AI explanation

For the quadratic equation ax^2 + bx + c = 0, the discriminant is D = b^2 - 4ac. If D = 0, the roots are real, equal, and rational (since a, b, c are rational numbers, the root -b/2a is also rational). Therefore, statements P and R are correct, meaning statements P and R are correct.

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