Class 9 Mathematics - Exploring Algebraic Identities - Quadratic expressions Hard Quiz

Mathematics Exploring Algebraic Identities Quadratic expressions Hard Class 9 Level 66

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Question 1/6 Hard Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 66

यदि \(x^2+11x+30\) को आयत क्षेत्र मॉडल से गुणनखंडित करना हो, तो कौन सी भुजाएं उचित हैं?

If \(x^2+11x+30\) is to be factorised using a rectangle area model, which sides are suitable?

Explanation opens after your attempt
Correct Answer

A. (x+5) और (x+6)(x+5) and (x+6)

Step 1

Concept

\(5\cdot6=30\) and (5+6=11). So the rectangle sides are (x+5) and (x+6).

Step 2

Why this answer is correct

The correct answer is A. (x+5) और (x+6) / (x+5) and (x+6). \(5\cdot6=30\) and (5+6=11). So the rectangle sides are (x+5) and (x+6).

Step 3

Exam Tip

\(5\cdot6=30\) और (5+6=11) है। इसलिए आयत की भुजाएं (x+5) और (x+6) होंगी।

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Question 2/6 Hard Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 66

आयत मॉडल में \(x^2-13x+40\) को दो भुजाओं में लिखने के लिए कौन सा विकल्प सही है?

In a rectangle model, which option correctly writes \(x^2-13x+40\) as two sides?

Explanation opens after your attempt
Correct Answer

A. (x-5) और (x-8)(x-5) and (x-8)

Step 1

Concept

((-5)+(-8)=-13) and ((-5)(-8)=40). Exam tip: with negative rectangles, the constant term can be positive.

Step 2

Why this answer is correct

The correct answer is A. (x-5) और (x-8) / (x-5) and (x-8). ((-5)+(-8)=-13) and ((-5)(-8)=40). Exam tip: with negative rectangles, the constant term can be positive.

Step 3

Exam Tip

((-5)+(-8)=-13) और ((-5)(-8)=40) है। परीक्षा में ऋण आयतों के साथ स्थिर पद धनात्मक हो सकता है।

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Question 3/6 Hard Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 66

यदि एक आयत मॉडल का कुल क्षेत्रफल \(2x^2+7x+3\) है, तो कौन सा भुजा युग्म सही हो सकता है?

If a rectangle model has total area \(2x^2+7x+3\), which pair of sides can be correct?

Explanation opens after your attempt
Correct Answer

B. (2x+3) और (x+1)(2x+3) and (x+1)

Step 1

Concept

((2x+3)(x+1)=2x-2+5x+3) is not correct, but ((2x+1)(x+3)=2x-2+7x+3) is correct. Exam tip: expand all options to check.

Step 2

Why this answer is correct

The correct answer is B. (2x+3) और (x+1) / (2x+3) and (x+1). ((2x+3)(x+1)=2x-2+5x+3) is not correct, but ((2x+1)(x+3)=2x-2+7x+3) is correct. Exam tip: expand all options to check.

Step 3

Exam Tip

((2x+3)(x+1)=2x-2+2x+3x+3=2x-2+5x+3) नहीं, लेकिन ((2x+1)(x+3)=2x-2+6x+x+3=2x-2+7x+3) है। परीक्षा में सभी विकल्प फैलाकर जांचें।

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Question 4/6 Hard Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 66

एक क्षेत्र मॉडल में \(2x^2+7x+3\) के लिए सही भुजाएं पहचाननी हैं। कौन सा विकल्प वास्तव में सही है?

In an area model for \(2x^2+7x+3\), the correct sides must be identified. Which option is actually correct?

Explanation opens after your attempt
Correct Answer

A. (2x+1) और (x+3)(2x+1) and (x+3)

Step 1

Concept

((2x+1)(x+3)=2x-2+6x+x+3=2x-2+7x+3). Exam tip: split the middle term into two parts.

Step 2

Why this answer is correct

The correct answer is A. (2x+1) और (x+3) / (2x+1) and (x+3). ((2x+1)(x+3)=2x-2+6x+x+3=2x-2+7x+3). Exam tip: split the middle term into two parts.

Step 3

Exam Tip

((2x+1)(x+3)=2x-2+6x+x+3=2x-2+7x+3) है। परीक्षा में मध्य पद को दो भागों में तोड़ें।

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Question 5/6 Hard Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 66

यदि \(6x^2+17x+12\) का आयत मॉडल बनाना हो, तो कौन सा गुणनफल सही क्षेत्र देता है?

If a rectangle model for \(6x^2+17x+12\) is to be made, which product gives the correct area?

Explanation opens after your attempt
Correct Answer

A. (2x+3) और (3x+4)(2x+3) and (3x+4)

Step 1

Concept

((2x+3)(3x+4)=6x-2+8x+9x+12=6x-2+17x+12). Exam tip: add the cross areas (8x) and (9x).

Step 2

Why this answer is correct

The correct answer is A. (2x+3) और (3x+4) / (2x+3) and (3x+4). ((2x+3)(3x+4)=6x-2+8x+9x+12=6x-2+17x+12). Exam tip: add the cross areas (8x) and (9x).

Step 3

Exam Tip

((2x+3)(3x+4)=6x-2+8x+9x+12=6x-2+17x+12) है। परीक्षा में क्रॉस क्षेत्र (8x) और (9x) जोड़ें।

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Question 6/6 Hard Mathematics Exploring Algebraic Identities Visual models of identities Class 9 Level 66

एक दृश्य मॉडल में ((x+a)(x+b)) का क्षेत्र \(x^2+9x+20\) है। (a) और (b) के संभावित मान कौन से हैं?

In a visual model, the area of ((x+a)(x+b)) is \(x^2+9x+20\). What can be the values of (a) and (b)?

Explanation opens after your attempt
Correct Answer

A. (4) और (5)(4) and (5)

Step 1

Concept

(4+5=9) and \(4\cdot5=20\). Exam tip: match the sum with the middle term and the product with the constant term.

Step 2

Why this answer is correct

The correct answer is A. (4) और (5) / (4) and (5). (4+5=9) and \(4\cdot5=20\). Exam tip: match the sum with the middle term and the product with the constant term.

Step 3

Exam Tip

(4+5=9) और \(4\cdot5=20\) है। परीक्षा में योग मध्य पद और गुणन स्थिर पद से मिलाएं।

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