If (p(x)=3x+a) and (q(x)=2x-5), what is (a) if the zero of (p(x)+q(x)) is (1)?
Answer and explanation
Correct answer: \(0\)
\(p(x)+q(x)=(3x+a)+(2x-5)=5x+a-5\). Since its zero is \(1\), put \(x=1\): \(5(1)+a-5=0\). Hence, \(a=0\). If \(a=1\), the polynomial has value \(1\), not zero, at \(x=1\). Exam tip: if \(r\) is a zero of a polynomial, substituting \(x=r\) must make the polynomial equal to \(0\).
Frequently asked questions
What is the correct answer to this question?
\(0\)
Why is this the correct answer?
\(p(x)+q(x)=(3x+a)+(2x-5)=5x+a-5\). Since its zero is \(1\), put \(x=1\): \(5(1)+a-5=0\). Hence, \(a=0\). If \(a=1\), the polynomial has value \(1\), not zero, at \(x=1\). Exam tip: if \(r\) is a zero of a polynomial, substituting \(x=r\) must make the polynomial equal to \(0\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Linear polynomials.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
