If the sum of roots of (3x^2+nx+12=0) is (-4), what is (n)?
Answer and explanation
Correct answer: (12)
For a quadratic equation ax^2 + bx + c = 0, the sum of its roots is -b/a. The minus sign is essential. In the equation 3x^2 + nx + 12 = 0, the leading coefficient is a = 3 and the coefficient of x is b = n. Therefore, the sum of roots is -n/3. The stated sum allows n to be found by a simple equation.
We are told that -n/3 = -4. Multiplying both sides by 3 gives -n = -12, and multiplying by -1 gives n = 12. Thus option A is correct. If the negative sign in the formula were missed, one might incorrectly obtain n = -12. The constant term 12 is not required for this calculation, because only the sum of roots is being used.
Frequently asked questions
What is the correct answer to this question?
(12)
Why is this the correct answer?
For a quadratic equation ax^2 + bx + c = 0, the sum of its roots is -b/a. The minus sign is essential. In the equation 3x^2 + nx + 12 = 0, the leading coefficient is a = 3 and the coefficient of x is b = n. Therefore, the sum of roots is -n/3. The stated sum allows n to be found by a simple equation.
We are told that -n/3 = -4. Multiplying both sides by 3 gives -n = -12, and multiplying by -1 gives n = 12. Thus option A is correct. If the negative sign in the formula were missed, one might incorrectly obtain n = -12. The constant term 12 is not required for this calculation, because only the sum of roots is being used.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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