Which statement is correct about the roots of 5x² = 0?
Answer and explanation
Correct answer: 0 is a repeated root
The governing concept is multiplicity of roots and the discriminant. Because 5 is nonzero, divide 5x² = 0 by 5 to obtain x² = 0, or (x − 0)² = 0. Thus the only distinct root is x = 0, and it occurs twice in the factorisation; it is therefore a repeated, or equal, root. The discriminant confirms this: for 5x² + 0x + 0 = 0, D = b² − 4ac = 0² − 4(5)(0) = 0, which indicates two equal real roots. Option B confuses the coefficient with a root, option C gives values that do not satisfy the equation, and option D is false because zero is a real number. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
0 is a repeated root
Why is this the correct answer?
The governing concept is multiplicity of roots and the discriminant. Because 5 is nonzero, divide 5x² = 0 by 5 to obtain x² = 0, or (x − 0)² = 0. Thus the only distinct root is x = 0, and it occurs twice in the factorisation; it is therefore a repeated, or equal, root. The discriminant confirms this: for 5x² + 0x + 0 = 0, D = b² − 4ac = 0² − 4(5)(0) = 0, which indicates two equal real roots. Option B confuses the coefficient with a root, option C gives values that do not satisfy the equation, and option D is false because zero is a real number. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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