For which value will the zero of ((k-7)x+14) be (-2)?
Answer and explanation
Correct answer: \(k=14\)
If \((-2)\) is a zero of \(((k-7)x+14)\), substituting \(x=-2\) must make the polynomial equal to 0: \((k-7)(-2)+14=0\). Thus, \(-2k+14+14=0\), or \(-2k+28=0\), which gives \(k=14\). For \(k=7\), the coefficient of \(x\) becomes 0 and the expression is 14, so it has no zero. Exam tip: When a zero is given, substitute it for \(x\) and equate the polynomial to 0.
Frequently asked questions
What is the correct answer to this question?
\(k=14\)
Why is this the correct answer?
If \((-2)\) is a zero of \(((k-7)x+14)\), substituting \(x=-2\) must make the polynomial equal to 0: \((k-7)(-2)+14=0\). Thus, \(-2k+14+14=0\), or \(-2k+28=0\), which gives \(k=14\). For \(k=7\), the coefficient of \(x\) becomes 0 and the expression is 14, so it has no zero. Exam tip: When a zero is given, substitute it for \(x\) and equate the polynomial to 0.
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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