Concept-wise Practice

cubic MCQ Questions for Class 10

cubic se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

Practice Questions

65 questions tagged with cubic.

यदि (p(x)=x-3+ax+b), (p(1)=6) और (p(-1)=-4), तो (a) का मान क्या है?

If (p(x)=x-3+ax+b), (p(1)=6), and (p(-1)=-4), what is the value of (a)?

Explanation opens after your attempt
Correct Answer

C. (4)

Step 1

Concept

The conditions give (1+a+b=6) and (-1-a+b=-4). Solving them gives (a=4).

Step 2

Why this answer is correct

The correct answer is C. (4). The conditions give (1+a+b=6) and (-1-a+b=-4). Solving them gives (a=4).

Step 3

Exam Tip

शर्तों से (1+a+b=6) और (-1-a+b=-4) मिलते हैं। इन्हें हल करने पर (a=4) मिलता है।

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किस मान के लिए (p(x)=x-3-5x-2+mx+8) में (p(1)=0) होगा?

For what value of (m) will (p(1)=0) in (p(x)=x-3-5x-2+mx+8)?

Explanation opens after your attempt
Correct Answer

A. (-4)

Step 1

Concept

(p(1)=1-5+m+8=m+4), so (m=-4). Substitute the given value and solve the equation.

Step 2

Why this answer is correct

The correct answer is A. (-4). (p(1)=1-5+m+8=m+4), so (m=-4). Substitute the given value and solve the equation.

Step 3

Exam Tip

(p(1)=1-5+m+8=m+4), इसलिए (m=-4)। दिए गए मान को रखकर समीकरण हल करें।

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(p(x)=3x-3-8x-2+7x-2) के लिए (p(2)) का मान क्या है?

What is the value of (p(2)) for (p(x)=3x-3-8x-2+7x-2)?

Explanation opens after your attempt
Correct Answer

B. (4)

Step 1

Concept

(p(2)=24-32+14-2=4). Evaluate each term separately and then add.

Step 2

Why this answer is correct

The correct answer is B. (4). (p(2)=24-32+14-2=4). Evaluate each term separately and then add.

Step 3

Exam Tip

(p(2)=24-32+14-2=4)। हर पद का मान अलग निकालकर जोड़ें।

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किस बहुपद के शून्यक (0), (2) और (-3) हैं?

Which polynomial has zeroes (0), (2), and (-3)?

Explanation opens after your attempt
Correct Answer

A. \(x^3+x^2-6x\)

Step 1

Concept

From the zeroes, the polynomial is (x(x-2)(x+3)). Expanding gives \(x^3+x^2-6x\).

Step 2

Why this answer is correct

The correct answer is A. \(x^3+x^2-6x\). From the zeroes, the polynomial is (x(x-2)(x+3)). Expanding gives \(x^3+x^2-6x\).

Step 3

Exam Tip

शून्यकों से बहुपद (x(x-2)(x+3)) बनेगा। इसे फैलाने पर \(x^3+x^2-6x\) मिलता है।

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बहुपद \(2x^3-9x^2+13x-6\) का एक गुणनखंड कौन सा है?

Which is a factor of \(2x^3-9x^2+13x-6\)?

Explanation opens after your attempt
Correct Answer

A. (x-1)

Step 1

Concept

(p(1)=2-9+13-6=0), so (x-1) is a factor. In option checking, try small values first.

Step 2

Why this answer is correct

The correct answer is A. (x-1). (p(1)=2-9+13-6=0), so (x-1) is a factor. In option checking, try small values first.

Step 3

Exam Tip

(p(1)=2-9+13-6=0) है इसलिए (x-1) गुणनखंड है। विकल्प जांच में छोटे मान पहले लगाएं।

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यदि (x-a), (x-b) और (x-c) किसी घन बहुपद के गुणनखंड हैं, तो उसका एक संभावित बहुपद कौन सा है?

If (x-a), (x-b), and (x-c) are factors of a cubic polynomial, which is a possible polynomial?

Explanation opens after your attempt
Correct Answer

A. (x-3-(a+b+c)x-2+(ab+bc+ca)x-abc)

Step 1

Concept

Expanding ((x-a)(x-b)(x-c)) gives the first form. Remember the link between zeroes and factors.

Step 2

Why this answer is correct

The correct answer is A. (x-3-(a+b+c)x-2+(ab+bc+ca)x-abc). Expanding ((x-a)(x-b)(x-c)) gives the first form. Remember the link between zeroes and factors.

Step 3

Exam Tip

((x-a)(x-b)(x-c)) फैलाने पर पहला रूप मिलता है। शून्यकों और गुणनखंडों का संबंध याद रखें।

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यदि (p(x)=x-3+px-2+qx-6) के शून्यक (1), (2) और (3) हैं, तो (p+q) का सही मान क्या है?

If the zeroes of (p(x)=x-3+px-2+qx-6) are (1), (2), and (3), what is the correct value of (p+q)?

Explanation opens after your attempt
Correct Answer

A. (5)

Step 1

Concept

From ((x-1)(x-2)(x-3)=x-3-6x-2+11x-6), (p=-6) and (q=11). Hence (p+q=5).

Step 2

Why this answer is correct

The correct answer is A. (5). From ((x-1)(x-2)(x-3)=x-3-6x-2+11x-6), (p=-6) and (q=11). Hence (p+q=5).

Step 3

Exam Tip

((x-1)(x-2)(x-3)=x-3-6x-2+11x-6) से (p=-6) और (q=11)। अतः (p+q=5) है।

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यदि (p(x)=x-3+px-2+qx-6) के शून्यक (1), (2) और (3) हैं, तो (p+q) का मान क्या है?

If the zeroes of (p(x)=x-3+px-2+qx-6) are (1), (2), and (3), what is (p+q)?

Explanation opens after your attempt
Correct Answer

A. (-5)

Step 1

Concept

The polynomial is ((x-1)(x-2)(x-3)=x-3-6x-2+11x-6). Hence (p=-6), (q=11), so (p+q=5).

Step 2

Why this answer is correct

The correct answer is A. (-5). The polynomial is ((x-1)(x-2)(x-3)=x-3-6x-2+11x-6). Hence (p=-6), (q=11), so (p+q=5).

Step 3

Exam Tip

बहुपद ((x-1)(x-2)(x-3)=x-3-6x-2+11x-6) है। इसलिए (p=-6), (q=11) और (p+q=5) नहीं बल्कि (5) है।

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बहुपद (p(x)=ax-3+bx-2+cx+d) में \(a\ne0\) है। यदि (p(x)) को रैखिक बहुपद कहा जाए, तो यह कथन क्यों गलत है?

In the polynomial (p(x)=ax-3+bx-2+cx+d), \(a\ne0\). Why is it wrong to call (p(x)) a linear polynomial?

Explanation opens after your attempt
Correct Answer

C. क्योंकि घात (3) हैBecause degree is (3)

Step 1

Concept

The highest power is (3), so the polynomial is cubic. In exams, always check the highest non-zero exponent.

Step 2

Why this answer is correct

The correct answer is C. क्योंकि घात (3) है / Because degree is (3). The highest power is (3), so the polynomial is cubic. In exams, always check the highest non-zero exponent.

Step 3

Exam Tip

सबसे बड़ी घात (3) है इसलिए बहुपद घन है। परीक्षा में हमेशा सबसे बड़े शून्येतर घातांक को देखें।

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(p(x)=2x-3+x-2-5x+2) में (p(2)) और (p(-1)) का अंतर (p(2)-p(-1)) क्या है?

For (p(x)=2x-3+x-2-5x+2), what is the difference (p(2)-p(-1))?

Explanation opens after your attempt
Correct Answer

D. (6)

Step 1

Concept

(p(2)=16+4-10+2=12) and (p(-1)=-2+1+5+2=6), so the difference is (6). Find both values separately.

Step 2

Why this answer is correct

The correct answer is D. (6). (p(2)=16+4-10+2=12) and (p(-1)=-2+1+5+2=6), so the difference is (6). Find both values separately.

Step 3

Exam Tip

(p(2)=16+4-10+2=12) और (p(-1)=-2+1+5+2=6), इसलिए अंतर (6) है। दोनों मान अलग निकालें।

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(p(x)=2x-3+x-2-5x+2) में (p(1)) और (p(-1)) का गुणनफल क्या है?

What is the product of (p(1)) and (p(-1)) for (p(x)=2x-3+x-2-5x+2)?

Explanation opens after your attempt
Correct Answer

A. (-12)

Step 1

Concept

(p(1)=2+1-5+2=0), and (p(-1)=-2+1+5+2=6), so the product is (0). The correct option is (0).

Step 2

Why this answer is correct

The correct answer is A. (-12). (p(1)=2+1-5+2=0), and (p(-1)=-2+1+5+2=6), so the product is (0). The correct option is (0).

Step 3

Exam Tip

(p(1)=0) नहीं बल्कि (2+1-5+2=0), और (p(-1)=-2+1+5+2=6), इसलिए गुणनफल (0) है। सही विकल्प (0) है।

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यदि (p(x)=x-3-3x-2+3x-1), तो (p(2)) क्या है?

If (p(x)=x-3-3x-2+3x-1), what is (p(2))?

Explanation opens after your attempt
Correct Answer

B. (1)

Step 1

Concept

It is ((x-1)3), so (p(2)=(2-1)3=1). Recognizing identities reduces calculation.

Step 2

Why this answer is correct

The correct answer is B. (1). It is ((x-1)3), so (p(2)=(2-1)3=1). Recognizing identities reduces calculation.

Step 3

Exam Tip

यह ((x-1)3) है, इसलिए (p(2)=(2-1)3=1)। पहचान पहचानने से गणना कम होती है।

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यदि (p(x)=x-3-4x), तो (p(-2)+p(2)) का मान क्या है?

If (p(x)=x-3-4x), what is the value of (p(-2)+p(2))?

Explanation opens after your attempt
Correct Answer

B. (0)

Step 1

Concept

(p(-2)=0) and (p(2)=0), so the sum is (0). It behaves like an odd polynomial.

Step 2

Why this answer is correct

The correct answer is B. (0). (p(-2)=0) and (p(2)=0), so the sum is (0). It behaves like an odd polynomial.

Step 3

Exam Tip

(p(-2)=0) और (p(2)=0), इसलिए योग (0) है। यह विषम बहुपद जैसा व्यवहार करता है।

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यदि (p(x)=x-3+ax-2+bx+4) में (x=1) और (x=-1) दोनों शून्य हैं, तो (a) क्या है?

If (x=1) and (x=-1) are both zeros of (p(x)=x-3+ax-2+bx+4), what is (a)?

Explanation opens after your attempt
Correct Answer

A. (-4)

Step 1

Concept

(p(1)=1+a+b+4=0) and (p(-1)=-1+a-b+4=0); adding gives (2a+8=0), so (a=-4). Add signs carefully.

Step 2

Why this answer is correct

The correct answer is A. (-4). (p(1)=1+a+b+4=0) and (p(-1)=-1+a-b+4=0); adding gives (2a+8=0), so (a=-4). Add signs carefully.

Step 3

Exam Tip

(p(1)=1+a+b+4=0) और (p(-1)=-1+a-b+4=0), इसलिए (2a+4=0) नहीं बल्कि जोड़ने पर (2a+8=0), अतः (a=-4)। संकेतों को सावधानी से जोड़ें।

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यदि (p(x)=x-3+ax-2+bx+6) में (x=1) और (x=-2) दोनों शून्य हैं, तो (a-b) क्या है?

If (x=1) and (x=-2) are both zeros of (p(x)=x-3+ax-2+bx+6), what is (a-b)?

Explanation opens after your attempt
Correct Answer

C. (4)

Step 1

Concept

The conditions give (a+b=-7) and (4a-2b=2), so (a=-2), (b=-5), and (a-b=3). The correct value is (3).

Step 2

Why this answer is correct

The correct answer is C. (4). The conditions give (a+b=-7) and (4a-2b=2), so (a=-2), (b=-5), and (a-b=3). The correct value is (3).

Step 3

Exam Tip

शर्तों से (a+b=-7) और (4a-2b=2), इसलिए (a=-2), (b=-5) और (a-b=3)। सही गणना से (a-b=3) मिलता है।

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(p(x)=x-3+x-2+x+1) के लिए (p(-1)) क्या है?

What is (p(-1)) for (p(x)=x-3+x-2+x+1)?

Explanation opens after your attempt
Correct Answer

B. (0)

Step 1

Concept

(p(-1)=-1+1-1+1=0). Add alternating signs in order.

Step 2

Why this answer is correct

The correct answer is B. (0). (p(-1)=-1+1-1+1=0). Add alternating signs in order.

Step 3

Exam Tip

(p(-1)=-1+1-1+1=0)। वैकल्पिक संकेतों को क्रम से जोड़ें।

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यदि (p(x)=x-3+rx-2+s), (p(0)=5) और (p(1)=9), तो (r) क्या है?

If (p(x)=x-3+rx-2+s), (p(0)=5), and (p(1)=9), what is (r)?

Explanation opens after your attempt
Correct Answer

C. (3)

Step 1

Concept

(p(0)=s=5) and (p(1)=1+r+5=9), so (r=3). First use (x=0) to find the constant term.

Step 2

Why this answer is correct

The correct answer is C. (3). (p(0)=s=5) and (p(1)=1+r+5=9), so (r=3). First use (x=0) to find the constant term.

Step 3

Exam Tip

(p(0)=s=5) और (p(1)=1+r+5=9), इसलिए (r=3)। पहले (x=0) से अचर पद निकालें।

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यदि (p(x)=x-3+px+q), (p(1)=4) और (p(-1)=-2), तो (p) का मान क्या है?

If (p(x)=x-3+px+q), (p(1)=4), and (p(-1)=-2), what is the value of (p)?

Explanation opens after your attempt
Correct Answer

B. (2)

Step 1

Concept

The conditions give (1+p+q=4) and (-1-p+q=-2), so (p=2). Subtracting the two equations is quick.

Step 2

Why this answer is correct

The correct answer is B. (2). The conditions give (1+p+q=4) and (-1-p+q=-2), so (p=2). Subtracting the two equations is quick.

Step 3

Exam Tip

शर्तों से (1+p+q=4) और (-1-p+q=-2), इसलिए (p=2)। दो समीकरणों को घटाना तेज तरीका है।

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किस मान के लिए (p(x)=x-3-4x-2+mx+6) में (p(1)=0) होगा?

For what value of (m) will (p(1)=0) in (p(x)=x-3-4x-2+mx+6)?

Explanation opens after your attempt
Correct Answer

A. (-3)

Step 1

Concept

(p(1)=1-4+m+6=m+3), so (m=-3). Substitute the given value and form a simple equation.

Step 2

Why this answer is correct

The correct answer is A. (-3). (p(1)=1-4+m+6=m+3), so (m=-3). Substitute the given value and form a simple equation.

Step 3

Exam Tip

(p(1)=1-4+m+6=m+3), इसलिए (m=-3)। दिए गए मान को रखकर सरल समीकरण बनाएं।

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(p(x)=2x-3-9x-2+12x-5) के लिए (p(2)) का मान क्या है?

What is the value of (p(2)) for (p(x)=2x-3-9x-2+12x-5)?

Explanation opens after your attempt
Correct Answer

A. (-1)

Step 1

Concept

(p(2)=16-36+24-5=-1). Evaluate each term separately and then add.

Step 2

Why this answer is correct

The correct answer is A. (-1). (p(2)=16-36+24-5=-1). Evaluate each term separately and then add.

Step 3

Exam Tip

(p(2)=16-36+24-5=-1)। प्रत्येक पद का मान अलग निकालकर जोड़ें।

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कौन सा व्यंजक (x) में बहुपद है लेकिन (x) में द्विघात नहीं है?

Which expression is a polynomial in (x) but not quadratic in (x)?

Explanation opens after your attempt
Correct Answer

B. \(6x^3-2x+9\)

Step 1

Concept

\(6x^3-2x+9\) is a polynomial and its degree is (3), so it is not quadratic. Classify by degree.

Step 2

Why this answer is correct

The correct answer is B. \(6x^3-2x+9\). \(6x^3-2x+9\) is a polynomial and its degree is (3), so it is not quadratic. Classify by degree.

Step 3

Exam Tip

\(6x^3-2x+9\) बहुपद है और इसकी घात (3) है, इसलिए यह द्विघात नहीं है। घात से वर्गीकरण करें।

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कौन सा कथन (p(x)=x-3+1) के बारे में सही है?

Which statement about (p(x)=x-3+1) is correct?

Explanation opens after your attempt
Correct Answer

C. यह घन बहुपद हैIt is a cubic polynomial

Step 1

Concept

In (p(x)=x-3+1), the highest power is (3), so it is a cubic polynomial. Decide the type of a polynomial by its degree.

Step 2

Why this answer is correct

The correct answer is C. यह घन बहुपद है / It is a cubic polynomial. In (p(x)=x-3+1), the highest power is (3), so it is a cubic polynomial. Decide the type of a polynomial by its degree.

Step 3

Exam Tip

(p(x)=x-3+1) में सबसे बड़ी घात (3) है इसलिए यह घन बहुपद है। बहुपद का प्रकार उसकी घात से तय करें।

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(q(x)=x-3+2x-2-5x-6) के लिए (q(-2)) क्या होगा?

For (q(x)=x-3+2x-2-5x-6), what is (q(-2))?

Explanation opens after your attempt
Correct Answer

C. (4)

Step 1

Concept

(q(-2)=-8+8+10-6=4). Check the sign of every term separately when substituting a negative value.

Step 2

Why this answer is correct

The correct answer is C. (4). (q(-2)=-8+8+10-6=4). Check the sign of every term separately when substituting a negative value.

Step 3

Exam Tip

(q(-2)=-8+8+10-6=4)। ऋणात्मक मान रखते समय प्रत्येक पद का संकेत अलग जांचें।

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(p(x)=2x-3+3x-2-5) में (x) का गुणांक क्या है?

What is the coefficient of (x) in (p(x)=2x-3+3x-2-5)?

Explanation opens after your attempt
Correct Answer

C. (0)

Step 1

Concept

There is no (x)-term, so its coefficient is (0). Treat the missing term as (0x).

Step 2

Why this answer is correct

The correct answer is C. (0). There is no (x)-term, so its coefficient is (0). Treat the missing term as (0x).

Step 3

Exam Tip

इसमें (x) का पद उपस्थित नहीं है इसलिए उसका गुणांक (0) है। अनुपस्थित पद को (0x) समझें।

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कौन सा विकल्प एक चर में बहुपद है लेकिन द्विघात नहीं है?

Which option is a polynomial in one variable but not quadratic?

Explanation opens after your attempt
Correct Answer

B. \(4x^3+x-9\)

Step 1

Concept

\(4x^3+x-9\) is a polynomial and its degree is (3). Therefore it is not quadratic.

Step 2

Why this answer is correct

The correct answer is B. \(4x^3+x-9\). \(4x^3+x-9\) is a polynomial and its degree is (3). Therefore it is not quadratic.

Step 3

Exam Tip

\(4x^3+x-9\) बहुपद है और इसकी घात (3) है। इसलिए यह द्विघात नहीं है।

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यदि किसी बहुपद की घात (3) है, तो उसे क्या कहते हैं?

If a polynomial has degree (3), what is it called?

Explanation opens after your attempt
Correct Answer

A. घन बहुपदCubic polynomial

Step 1

Concept

A degree (3) polynomial is called a cubic polynomial. The highest power decides the name.

Step 2

Why this answer is correct

The correct answer is A. घन बहुपद / Cubic polynomial. A degree (3) polynomial is called a cubic polynomial. The highest power decides the name.

Step 3

Exam Tip

घात (3) वाला बहुपद घन बहुपद कहलाता है। सबसे बड़ी घात ही नाम तय करती है।

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\(2x^3+x^2+x+8\) किस प्रकार का बहुपद है?

What type of polynomial is \(2x^3+x^2+x+8\)?

Explanation opens after your attempt
Correct Answer

C. घनCubic

Step 1

Concept

The highest power is (3), so it is a cubic polynomial. Classify a polynomial by its degree.

Step 2

Why this answer is correct

The correct answer is C. घन / Cubic. The highest power is (3), so it is a cubic polynomial. Classify a polynomial by its degree.

Step 3

Exam Tip

सबसे बड़ी घात (3) है इसलिए यह घन बहुपद है। बहुपद का प्रकार उसकी घात से तय करें।

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यदि (p(x)=x-3-3x), तो (p\(\sqrt{3}\)) का मान क्या है?

If (p(x)=x-3-3x), what is (p\(\sqrt{3}\))?

Explanation opens after your attempt
Correct Answer

A. (0)

Step 1

Concept

(\(\sqrt{3}\)3=3\sqrt{3}), so \(3\sqrt{3}-3\sqrt{3}=0\). Simplifying powers is the key step in such questions.

Step 2

Why this answer is correct

The correct answer is A. (0). (\(\sqrt{3}\)3=3\sqrt{3}), so \(3\sqrt{3}-3\sqrt{3}=0\). Simplifying powers is the key step in such questions.

Step 3

Exam Tip

(\(\sqrt{3}\)3=3\sqrt{3}), इसलिए \(3\sqrt{3}-3\sqrt{3}=0\) है। परीक्षा में ऐसे प्रश्नों में घात को सरल करना मुख्य कदम है।

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यदि बहुपद (p(x)=5(x+1)(x-2)(x-4)) है तो ग्राफ (x)-अक्ष को कितने अलग बिंदुओं पर काटेगा?

If (p(x)=5(x+1)(x-2)(x-4)), at how many distinct points will the graph cut the (x)-axis?

Explanation opens after your attempt
Correct Answer

A. तीनThree

Step 1

Concept

The factors give zeroes (-1), (2), and (4). Three distinct zeroes give three distinct (x)-intercepts.

Step 2

Why this answer is correct

The correct answer is A. तीन / Three. The factors give zeroes (-1), (2), and (4). Three distinct zeroes give three distinct (x)-intercepts.

Step 3

Exam Tip

गुणनखंडों से शून्यक (-1), (2), और (4) हैं। तीन अलग शून्यक तीन अलग (x)-प्रतिच्छेद देते हैं।

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ग्राफ (x)-अक्ष को ((-2,0)), ((0,0)), और ((5,0)) पर काटता है। कौन सा कथन सही है?

The graph cuts the (x)-axis at ((-2,0)), ((0,0)), and ((5,0)). Which statement is correct?

Explanation opens after your attempt
Correct Answer

A. शून्यक (-2,0,5) हैंThe zeroes are (-2,0,5)

Step 1

Concept

The origin also lies on the (x)-axis so (0) is also a zero. Write the (x)-values of all intercepts.

Step 2

Why this answer is correct

The correct answer is A. शून्यक (-2,0,5) हैं / The zeroes are (-2,0,5). The origin also lies on the (x)-axis so (0) is also a zero. Write the (x)-values of all intercepts.

Step 3

Exam Tip

मूल बिंदु भी (x)-अक्ष पर है इसलिए (0) भी शून्यक है। सभी (x)-प्रतिच्छेदों के (x)-मान लिखें।

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