What is the correct statement about the real roots of x² + 25 = 0?
Answer and explanation
Correct answer: There are no real roots
The governing concept is the non-negative-square property: for every real number x, x² is greater than or equal to zero. Rearranging the equation x² + 25 = 0 gives x² = −25. A real square cannot equal a negative number, so no real value of x can satisfy this equation. Equivalently, the discriminant for x² + 25 = 0 is 0² − 4(1)(25) = −100, which is negative and therefore confirms the absence of real roots. Hence option A is correct. Although 5 and −5 are related to the square of 25, they solve x² − 25 = 0, not x² + 25 = 0. The other options also contradict the equation.
Frequently asked questions
What is the correct answer to this question?
There are no real roots
Why is this the correct answer?
The governing concept is the non-negative-square property: for every real number x, x² is greater than or equal to zero. Rearranging the equation x² + 25 = 0 gives x² = −25. A real square cannot equal a negative number, so no real value of x can satisfy this equation. Equivalently, the discriminant for x² + 25 = 0 is 0² − 4(1)(25) = −100, which is negative and therefore confirms the absence of real roots. Hence option A is correct. Although 5 and −5 are related to the square of 25, they solve x² − 25 = 0, not x² + 25 = 0. The other options also contradict the equation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
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