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factor theorem MCQ Questions for Class 10

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2 questions tagged with factor theorem.

Question 1/2 Expert Mathematics Chapter 2: Polynomials Irrational numbers and real numbers Class 10 Level 26

यदि \(2+\sqrt{3}\) किसी परिमेय गुणांक वाले बहुपद का शून्यक है, तो किस रैखिक गुणनखंड का साथ आना अपेक्षित है?

If \(2+\sqrt{3}\) is a zero of a polynomial with rational coefficients, which linear factor is expected to accompany it?

Explanation opens after your attempt
Correct Answer

A. (x-\(2-\sqrt{3}\))

Step 1

Concept

The companion zero is \(2-\sqrt{3}\), so the factor is (x-\(2-\sqrt{3}\)). In exams remember the relation between a zero and factor as \(x-\alpha\).

Step 2

Why this answer is correct

The correct answer is A. (x-\(2-\sqrt{3}\)). The companion zero is \(2-\sqrt{3}\), so the factor is (x-\(2-\sqrt{3}\)). In exams remember the relation between a zero and factor as \(x-\alpha\).

Step 3

Exam Tip

साथी शून्यक \(2-\sqrt{3}\) होगा, इसलिए गुणनखंड (x-\(2-\sqrt{3}\)) है। परीक्षा में शून्यक और गुणनखंड का संबंध \(x-\alpha\) याद रखें।

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Question 2/2 Medium Mathematics Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22

यदि (p(x)=x(x-5)), तो ग्राफ किन (x)-मानों पर (x)-अक्ष को काटेगा?

If (p(x)=x(x-5)), at which (x)-values will the graph cut the (x)-axis?

Explanation opens after your attempt
Correct Answer

A. (0) और (5)(0) and (5)

Step 1

Concept

From (x=0) or (x-5=0), we get (x=0,5). Tip: if a product is zero, at least one factor is zero.

Step 2

Why this answer is correct

The correct answer is A. (0) और (5) / (0) and (5). From (x=0) or (x-5=0), we get (x=0,5). Tip: if a product is zero, at least one factor is zero.

Step 3

Exam Tip

(x=0) या (x-5=0) से (x=0,5) मिलते हैं। टिप: गुणनफल शून्य हो तो कम से कम एक कारक शून्य होता है।

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