For which value will ((r²−5r+6)x+4) not remain a linear polynomial?
Answer and explanation
Correct answer: r=2 या r=3
A polynomial of the form ax+b is linear only when the coefficient a is nonzero. Here the coefficient of x is r²−5r+6. For the expression to stop being linear, this coefficient must equal zero. Solve r²−5r+6=0 by factorisation: (r−2)(r−3)=0. Hence r=2 or r=3. In either case the x-term disappears and the expression becomes the constant 4, which has degree 0 rather than degree 1. Therefore option A is correct. The values in option B do not make the coefficient zero, option C is incomplete and incorrect, and option D is false because two valid values exist.
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What is the correct answer to this question?
r=2 या r=3
Why is this the correct answer?
A polynomial of the form ax+b is linear only when the coefficient a is nonzero. Here the coefficient of x is r²−5r+6. For the expression to stop being linear, this coefficient must equal zero. Solve r²−5r+6=0 by factorisation: (r−2)(r−3)=0. Hence r=2 or r=3. In either case the x-term disappears and the expression becomes the constant 4, which has degree 0 rather than degree 1. Therefore option A is correct. The values in option B do not make the coefficient zero, option C is incomplete and incorrect, and option D is false because two valid values exist.
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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