If both roots of (x^2+4x+c=0) are real and negative, which condition is necessary and sufficient?

The sum (-4) is already negative and the product must be positive, so (c>0). For real roots, (16-4c\ge0), hence (0<c\le4).

This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.

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Correct answer: (0<c\le4)

The sum (-4) is already negative and the product must be positive, so (c>0). For real roots, (16-4c\ge0), hence (0<c\le4).

What is the correct answer to this question?

(0<c\le4)

Why is this the correct answer?

The sum (-4) is already negative and the product must be positive, so (c>0). For real roots, (16-4c\ge0), hence (0<c\le4).

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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