If 2 is a root of x² + kx − 14 = 0, what is the value of k?
Answer and explanation
Correct answer: 5
Because x = 2 is a root, substituting x = 2 must make the quadratic expression equal to zero. Thus 2² + k(2) − 14 = 0. Simplifying gives 4 + 2k − 14 = 0, so 2k − 10 = 0. Therefore 2k = 10 and k = 5. Option A is correct. The constant term is already −14 and should not be changed; only the given root is substituted into the x terms. Option B results from an incorrect sign, while options C and D do not satisfy the equation when k is checked by substitution.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
Because x = 2 is a root, substituting x = 2 must make the quadratic expression equal to zero. Thus 2² + k(2) − 14 = 0. Simplifying gives 4 + 2k − 14 = 0, so 2k − 10 = 0. Therefore 2k = 10 and k = 5. Option A is correct. The constant term is already −14 and should not be changed; only the given root is substituted into the x terms. Option B results from an incorrect sign, while options C and D do not satisfy the equation when k is checked by substitution.
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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