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14 results found for "polynomial-formation" in Class 10.

Question Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 27

किस द्विघात बहुपद के शून्यक \(2+\sqrt{10}\) और \(2-\sqrt{10}\) हैं?

Which quadratic polynomial has zeroes \(2+\sqrt{10}\) and \(2-\sqrt{10}\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-4x-6\)

Step 1

Concept

The sum is (4) and the product is (4-10=-6). Hence the polynomial is \(x^2-4x-6\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-4x-6\). The sum is (4) and the product is (4-10=-6). Hence the polynomial is \(x^2-4x-6\).

Step 3

Exam Tip

योग (4) और गुणनफल (4-10=-6) है। इसलिए बहुपद \(x^2-4x-6\) होगा।

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Question Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

किस विकल्प में बहुपद के सभी गुणांक परिमेय हैं और शून्यक \(6+\sqrt{11}\) तथा \(6-\sqrt{11}\) हैं?

Which option has all rational coefficients and zeroes \(6+\sqrt{11}\) and \(6-\sqrt{11}\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-12x+25\)

Step 1

Concept

The sum is (12) and the product is (36-11=25), so the polynomial is \(x^2-12x+25\). In exams write the standard form correctly.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-12x+25\). The sum is (12) and the product is (36-11=25), so the polynomial is \(x^2-12x+25\). In exams write the standard form correctly.

Step 3

Exam Tip

योग (12) और गुणनफल (36-11=25) है, इसलिए बहुपद \(x^2-12x+25\) है। परीक्षा में मानक रूप ठीक से लिखें।

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Question Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

कौन सा बहुपद \(1+\sqrt{6}\) और \(1-\sqrt{6}\) को शून्यक रखता है?

Which polynomial has \(1+\sqrt{6}\) and \(1-\sqrt{6}\) as zeroes?

Explanation opens after your attempt
Correct Answer

A. \(x^2-2x-5\)

Step 1

Concept

The sum is (2) and the product is (1-6=-5), so the polynomial is \(x^2-2x-5\). In exams use \(a^2-b^2\) for the product.

Step 2

Why this answer is correct

The correct answer is A. \(x^2-2x-5\). The sum is (2) and the product is (1-6=-5), so the polynomial is \(x^2-2x-5\). In exams use \(a^2-b^2\) for the product.

Step 3

Exam Tip

योग (2) और गुणनफल (1-6=-5) है, इसलिए बहुपद \(x^2-2x-5\) है। परीक्षा में गुणनफल में \(a^2-b^2\) लगाएं।

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Question Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

किस द्विघात बहुपद के शून्यक \(3+\sqrt{2}\) और \(3-\sqrt{2}\) हैं?

Which quadratic polynomial has zeroes \(3+\sqrt{2}\) and \(3-\sqrt{2}\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-6x+7\)

Step 1

Concept

\(The sum is (6) and the product is (7), so the polynomial is (x^2-6x+7). In exams use (x^2-(\)sum)x+product).

Step 2

Why this answer is correct

\(The correct answer is A. (x^2-6x+7). The sum is (6) and the product is (7), so the polynomial is (x^2-6x+7). In exams use (x^2-(\)sum)x+product).

Step 3

Exam Tip

योग (6) और गुणनफल (7) है, इसलिए बहुपद \(x^2-6x+7\) है। \(परीक्षा में (x^2-(\)योग)x+गुणनफल) प्रयोग करें।

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Question Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

यदि शून्यक \(\frac{3+\sqrt{5}}{2}\) और \(\frac{3-\sqrt{5}}{2}\) हैं, तो एकक बहुपद क्या है?

If the zeroes are \(\frac{3+\sqrt{5}}{2}\) and \(\frac{3-\sqrt{5}}{2}\), what is the monic polynomial?

Explanation opens after your attempt
Correct Answer

A. \(x^2-3x+1\)

Step 1

Concept

The sum is (3) and the product is \(\frac{9-5}{4}=1\). Therefore the polynomial is \(x^2-3x+1\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-3x+1\). The sum is (3) and the product is \(\frac{9-5}{4}=1\). Therefore the polynomial is \(x^2-3x+1\).

Step 3

Exam Tip

योग (3) और गुणनफल \(\frac{9-5}{4}=1\) है। इसलिए बहुपद \(x^2-3x+1\) है।

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Question Expert Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 25

किस बहुपद के शून्यक \(3+\sqrt{2}\) और \(3-\sqrt{2}\) हैं?

Which polynomial has zeroes \(3+\sqrt{2}\) and \(3-\sqrt{2}\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-6x+7\)

Step 1

Concept

The sum is (6) and the product is (9-2=7). The polynomial is \(x^2-6x+7\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-6x+7\). The sum is (6) and the product is (9-2=7). The polynomial is \(x^2-6x+7\).

Step 3

Exam Tip

योग (6) और गुणनफल (9-2=7) है। बहुपद \(x^2-6x+7\) होगा।

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Question Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 27

यदि किसी द्विघात बहुपद के शून्यक \(5+\sqrt{2}\) और \(5-\sqrt{2}\) हैं, तो बहुपद क्या होगा?

If the zeroes of a quadratic polynomial are \(5+\sqrt{2}\) and \(5-\sqrt{2}\), what is the polynomial?

Explanation opens after your attempt
Correct Answer

A. \(x^2-10x+23\)

Step 1

Concept

The sum is (10) and the product is (25-2=23). Therefore the polynomial is \(x^2-10x+23\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-10x+23\). The sum is (10) and the product is (25-2=23). Therefore the polynomial is \(x^2-10x+23\).

Step 3

Exam Tip

योग (10) और गुणनफल (25-2=23) है। इसलिए बहुपद \(x^2-10x+23\) होगा।

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Question Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

यदि किसी परिमेय गुणांकों वाले द्विघात बहुपद का एक शून्यक \(6-2\sqrt{5}\) है, तो उस बहुपद का एक संभव रूप क्या है?

If one zero of a quadratic polynomial with rational coefficients is \(6-2\sqrt{5}\), what is one possible form of that polynomial?

Explanation opens after your attempt
Correct Answer

A. \(x^2-12x+16\)

Step 1

Concept

The other zero is \(6+2\sqrt{5}\). The sum is (12) and product is (36-20=16), so the polynomial is \(x^2-12x+16\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-12x+16\). The other zero is \(6+2\sqrt{5}\). The sum is (12) and product is (36-20=16), so the polynomial is \(x^2-12x+16\).

Step 3

Exam Tip

दूसरा शून्यक \(6+2\sqrt{5}\) होगा। योग (12) और गुणनफल (36-20=16), इसलिए बहुपद \(x^2-12x+16\) है।

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Question Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 26

किस बहुपद के शून्यकों का योग \(5\sqrt{2}\) और गुणनफल (12) है?

Which polynomial has zeroes with sum \(5\sqrt{2}\) and product (12)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-5\sqrt{2}x+12\)

Step 1

Concept

The polynomial is \(x^2-Sx+P\). Here \(S=5\sqrt{2}\) and (P=12).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-5\sqrt{2}x+12\). The polynomial is \(x^2-Sx+P\). Here \(S=5\sqrt{2}\) and (P=12).

Step 3

Exam Tip

बहुपद \(x^2-Sx+P\) होता है। यहाँ \(S=5\sqrt{2}\) और (P=12) हैं।

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Question Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 28

यदि शून्यकों का योग \(2\sqrt{5}\) और गुणनफल (4) है, तो एक मानक द्विघात बहुपद कौन सा होगा?

If the sum of zeroes is \(2\sqrt{5}\) and the product is (4), which is a monic quadratic polynomial?

Explanation opens after your attempt
Correct Answer

A. \(x^2-2\sqrt{5}x+4\)

Step 1

Concept

\(A monic polynomial is (x^2-(\)sum)x+product\(). So the answer is (x^2-2\sqrt{5}x+4).\)

Step 2

Why this answer is correct

\(The correct answer is A. (x^2-2\sqrt{5}x+4). A monic polynomial is (x^2-(\)sum)x+product\(). So the answer is (x^2-2\sqrt{5}x+4).\)

Step 3

Exam Tip

\(मानक बहुपद (x^2-(\)योग)x+गुणनफल) होता है। \(इसलिए उत्तर (x^2-2\sqrt{5}x+4) है\)।

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Question Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 28

किस बहुपद के शून्यक \(\sqrt{2}+\sqrt{3}\) और \(\sqrt{2}-\sqrt{3}\) हैं?

Which polynomial has zeroes \(\sqrt{2}+\sqrt{3}\) and \(\sqrt{2}-\sqrt{3}\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-2\sqrt{2}x-1\)

Step 1

Concept

The sum is \(2\sqrt{2}\) and the product is (2-3=-1). Hence the polynomial is \(x^2-2\sqrt{2}x-1\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-2\sqrt{2}x-1\). The sum is \(2\sqrt{2}\) and the product is (2-3=-1). Hence the polynomial is \(x^2-2\sqrt{2}x-1\).

Step 3

Exam Tip

योग \(2\sqrt{2}\) और गुणनफल (2-3=-1) है। इसलिए बहुपद \(x^2-2\sqrt{2}x-1\) बनेगा।

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Question Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 28

किस बहुपद के शून्यक \(1+\sqrt{2}\) और \(1-\sqrt{2}\) हैं?

Which polynomial has zeroes \(1+\sqrt{2}\) and \(1-\sqrt{2}\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-2x-1\)

Step 1

Concept

The sum is (2) and the product is (-1). So the polynomial is \(x^2-2x-1\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-2x-1\). The sum is (2) and the product is (-1). So the polynomial is \(x^2-2x-1\).

Step 3

Exam Tip

योग (2) और गुणनफल (-1) है। इसलिए बहुपद \(x^2-2x-1\) है।

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Question Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 28

यदि \(2+\sqrt{3}\) और \(2-\sqrt{3}\) किसी द्विघात बहुपद के शून्यक हैं, तो बहुपद क्या होगा?

If \(2+\sqrt{3}\) and \(2-\sqrt{3}\) are zeroes of a quadratic polynomial, what is the polynomial?

Explanation opens after your attempt
Correct Answer

A. \(x^2-4x+1\)

Step 1

Concept

The sum is (4) and the product is (1). Therefore the polynomial is \(x^2-4x+1\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-4x+1\). The sum is (4) and the product is (1). Therefore the polynomial is \(x^2-4x+1\).

Step 3

Exam Tip

योग (4) और गुणनफल (1) है। अतः बहुपद \(x^2-4x+1\) है।

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Question Hard Mathematics Polynomials Irrational numbers and real numbers Class 10 Level 28

किस बहुपद के शून्यक \(\sqrt{7}\) और \(-\sqrt{7}\) हैं?

Which polynomial has zeroes \(\sqrt{7}\) and \(-\sqrt{7}\)?

Explanation opens after your attempt
Correct Answer

A. \(x^2-7\)

Step 1

Concept

The sum of zeroes is (0) and the product is (-7). Hence the polynomial is \(x^2-7\).

Step 2

Why this answer is correct

The correct answer is A. \(x^2-7\). The sum of zeroes is (0) and the product is (-7). Hence the polynomial is \(x^2-7\).

Step 3

Exam Tip

शून्यकों का योग (0) और गुणनफल (-7) है। इसलिए बहुपद \(x^2-7\) होगा।

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