Question

One root of a quadratic equation is 3 + `sqrt2`.

Statement (1): The other root of the given quadratic equation is 3 − `sqrt2`.

Statement (2): If one root of the given quadratic equation is in the form of a surd, the other root is its conjugate.

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Both the statements are true.

Explanation:

We are given that one root of the quadratic equation is 3 + `sqrt2`. Since the equation has real coefficients, the conjugate of a surd root must also be a root.

Therefore, the other root is 3 − `sqrt2`.

Hence, statement (1) is true.

The conjugate root property applies to quadratic equations with real coefficients. Thus, if one root is 3 + `sqrt2`, the other root must be its conjugate, 3 − `sqrt2`.

Hence, statement (2) is also true.