For which value of r will (2r + 5)x − 10 not remain a linear polynomial?
Answer and explanation
Correct answer: r = −5/2
A polynomial in x is linear only when the coefficient of x is nonzero, because its degree must be exactly 1. In (2r + 5)x − 10, the coefficient of x is 2r + 5. For the expression to stop being linear, this coefficient must equal zero: 2r + 5 = 0, so 2r = −5 and r = −5/2. The expression then becomes −10, a constant polynomial of degree 0. Thus option B is correct. The other listed values leave a nonzero coefficient of x, so the degree remains 1.
Frequently asked questions
What is the correct answer to this question?
r = −5/2
Why is this the correct answer?
A polynomial in x is linear only when the coefficient of x is nonzero, because its degree must be exactly 1. In (2r + 5)x − 10, the coefficient of x is 2r + 5. For the expression to stop being linear, this coefficient must equal zero: 2r + 5 = 0, so 2r = −5 and r = −5/2. The expression then becomes −10, a constant polynomial of degree 0. Thus option B is correct. The other listed values leave a nonzero coefficient of x, so the degree remains 1.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Linear polynomials.
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