If the sum of roots of (4x^2+mx+20=0) is (-6), what is (m)?
Answer and explanation
Correct answer: (24)
The sum of roots of a quadratic equation ax^2 + bx + c = 0 is -b/a. In 4x^2 + mx + 20 = 0, a = 4 and b = m, so the sum is -m/4. The question gives this sum as -6. Equating these two expressions provides a direct linear equation for m. The constant term 20 is irrelevant because it is used for the product, not the sum.
Set -m/4 = -6. Multiplying by 4 gives -m = -24, and changing the signs gives m = 24. Therefore option A is correct. The answer would be -24 only if the leading negative sign in the root-sum formula were mishandled. Options C and D confuse the value of the root sum or its coefficient with the requested coefficient m.
Frequently asked questions
What is the correct answer to this question?
(24)
Why is this the correct answer?
The sum of roots of a quadratic equation ax^2 + bx + c = 0 is -b/a. In 4x^2 + mx + 20 = 0, a = 4 and b = m, so the sum is -m/4. The question gives this sum as -6. Equating these two expressions provides a direct linear equation for m. The constant term 20 is irrelevant because it is used for the product, not the sum.
Set -m/4 = -6. Multiplying by 4 gives -m = -24, and changing the signs gives m = 24. Therefore option A is correct. The answer would be -24 only if the leading negative sign in the root-sum formula were mishandled. Options C and D confuse the value of the root sum or its coefficient with the requested coefficient m.
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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