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600 questions tagged with quadratic equations.
What are (a), (b), (c) in \(7x^2-14=0\)?
A. (7,0,-14)
Write it as \(7x^2+0x-14=0\). Then (a=7), (b=0), (c=-14).
The correct answer is A. (7,0,-14). Write it as \(7x^2+0x-14=0\). Then (a=7), (b=0), (c=-14).
इसे \(7x^2+0x-14=0\) लिखें। इससे (a=7), (b=0), (c=-14) मिलते हैं।
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If (x=1), what is the left side of \(x^2+2x-3=0\)?
A. (0)
Substituting gives \(1^2+2\cdot1-3=0\). So (1) is a solution.
The correct answer is A. (0). Substituting gives \(1^2+2\cdot1-3=0\). So (1) is a solution.
रखने पर \(1^2+2\cdot1-3=0\) मिलता है। इसलिए (1) एक हल है।
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How do we write \(x^2-16=0\) in factor form?
A. \((x-4)(x+4)=0\)
\(x^2-16\) is a difference of squares. Hence it becomes ((x-4)(x+4)).
The correct answer is A. \((x-4)(x+4)=0\). \(x^2-16\) is a difference of squares. Hence it becomes ((x-4)(x+4)).
\(x^2-16\) वर्गों का अंतर है। इसलिए यह ((x-4)(x+4)) बनता है।
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Which equation is equivalent to \(x^2+2x+1=0\)?
A. \((x+1)^2=0\)
((x+1)2=x-2+2x+1). Recognising perfect squares helps solve faster.
The correct answer is A. \((x+1)^2=0\). ((x+1)2=x-2+2x+1). Recognising perfect squares helps solve faster.
((x+1)2=x-2+2x+1) होता है। पूर्ण वर्ग पहचानना तेजी से हल कराने में मदद करता है।
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What is the linear term in \(2x^2+0x-7=0\)?
B. (0x)
The linear term is the term containing (x). Here it is (0x).
The correct answer is B. (0x). The linear term is the term containing (x). Here it is (0x).
रैखिक पद (x) वाला पद होता है। यहां वह (0x) है।
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Which of the following contains the \(x^2\) term?
C. \(x^2-2=0\)
The \(x^2\) term is necessary for a quadratic equation. Option (C) has this term.
The correct answer is C. \(x^2-2=0\). The \(x^2\) term is necessary for a quadratic equation. Option (C) has this term.
द्विघात समीकरण के लिए \(x^2\) पद आवश्यक है। विकल्प (C) में यह पद है।
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If an equation in (x) has degree (2), what is it called?
B. द्विघात समीकरणQuadratic equation
An equation of degree (2) is called a quadratic equation. Remember that quadratic means degree (2).
The correct answer is B. द्विघात समीकरण / Quadratic equation. An equation of degree (2) is called a quadratic equation. Remember that quadratic means degree (2).
घात (2) वाले समीकरण को द्विघात समीकरण कहते हैं। नाम याद रखने के लिए द्वि का अर्थ (2) समझें।
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Which value is a solution of \(x^2+x-6=0\)?
B. (2)
Since \(2^2+2-6=0\), (x=2) is a solution of the equation.
The correct answer is B. (2). Since \(2^2+2-6=0\), (x=2) is a solution of the equation.
\(2^2+2-6=0\) है। इसलिए (x=2) इस समीकरण का हल है।
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Which option shows \(x^2+6x+9=0\) in factor form?
A. \((x+3)^2=0\)
\(x^2+6x+9\) is a perfect square. It equals ((x+3)2).
The correct answer is A. \((x+3)^2=0\). \(x^2+6x+9\) is a perfect square. It equals ((x+3)2).
\(x^2+6x+9\) एक पूर्ण वर्ग है। यह ((x+3)2) के बराबर है।
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What is the value of (a) in \(-x^2+3x+10=0\)?
B. \(-1\)
The coefficient of \(-x^2\) is (-1). So (a=-1).
The correct answer is B. \(-1\). The coefficient of \(-x^2\) is (-1). So (a=-1).
\(-x^2\) का गुणांक (-1) होता है। इसलिए (a=-1) है।
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What is the coefficient of \(x^2\) in \(x^2+8x+16=0\)?
B. (1)
When no number is written before \(x^2\), its coefficient is (1). This is a common exam mistake.
The correct answer is B. (1). When no number is written before \(x^2\), its coefficient is (1). This is a common exam mistake.
जब \(x^2\) के आगे कोई संख्या नहीं लिखी होती तब गुणांक (1) होता है। यह सामान्य परीक्षा गलती है।
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Which is the standard form of ((x-4)(x+1)=0)?
A. \(x^2-3x-4=0\)
Expanding gives \(x^2+x-4x-4=0\). So \(x^2-3x-4=0\) is correct.
The correct answer is A. \(x^2-3x-4=0\). Expanding gives \(x^2+x-4x-4=0\). So \(x^2-3x-4=0\) is correct.
विस्तार करने पर \(x^2+x-4x-4=0\) मिलता है। इसलिए \(x^2-3x-4=0\) सही है।
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What is the expanded form of ((x+2)(x+3)=0)?
A. \(x^2+5x+6=0\)
Expansion gives \(x^2+3x+2x+6=0\). Combining like terms gives \(x^2+5x+6=0\).
The correct answer is A. \(x^2+5x+6=0\). Expansion gives \(x^2+3x+2x+6=0\). Combining like terms gives \(x^2+5x+6=0\).
विस्तार से \(x^2+3x+2x+6=0\) मिलता है। समान पद जोड़कर \(x^2+5x+6=0\) बनता है।
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Write (x(x+5)=0) in standard form.
A. \(x^2+5x=0\)
Multiplying gives \(x^2+5x=0\). While opening brackets, multiply each term.
The correct answer is A. \(x^2+5x=0\). Multiplying gives \(x^2+5x=0\). While opening brackets, multiply each term.
गुणा करने पर \(x^2+5x=0\) मिलता है। कोष्ठक खोलते समय हर पद से गुणा करें।
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For \(6x^2=0\), what are (a), (b), (c) respectively?
A. (6,0,0)
It is written as \(6x^2+0x+0=0\). Therefore (a=6), (b=0), (c=0).
The correct answer is A. (6,0,0). It is written as \(6x^2+0x+0=0\). Therefore (a=6), (b=0), (c=0).
इसे \(6x^2+0x+0=0\) लिखा जाता है। इसलिए (a=6), (b=0), (c=0) हैं।
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Which equation is not quadratic?
C. \(x^3+x+1=0\)
The degree of \(x^3+x+1=0\) is (3). So it is not a quadratic equation.
The correct answer is C. \(x^3+x+1=0\). The degree of \(x^3+x+1=0\) is (3). So it is not a quadratic equation.
\(x^3+x+1=0\) की घात (3) है। इसलिए यह द्विघात समीकरण नहीं है।
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Which of the following is a quadratic polynomial?
B. \(x^2-3x+2\)
A quadratic polynomial has degree (2). In \(x^2-3x+2\), the highest power is (2).
The correct answer is B. \(x^2-3x+2\). A quadratic polynomial has degree (2). In \(x^2-3x+2\), the highest power is (2).
द्विघात बहुपद की घात (2) होती है। \(x^2-3x+2\) में सबसे बड़ी घात (2) है।
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What do we get by putting (x=2) in \(x^2-4x+4=0\)?
A. (0=0)
We get \(2^2-4\cdot2+4=0\). Hence (x=2) is a correct solution.
The correct answer is A. (0=0). We get \(2^2-4\cdot2+4=0\). Hence (x=2) is a correct solution.
\(2^2-4\cdot2+4=0\) है। अतः (x=2) सही हल है।
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Which value is one solution of \(x^2-9=0\)?
B. (3)
Since \(3^2-9=0\), (3) is a solution. For easy questions, check by substitution.
The correct answer is B. (3). Since \(3^2-9=0\), (3) is a solution. For easy questions, check by substitution.
\(3^2-9=0\) इसलिए (3) हल है। आसान प्रश्नों में मान रखकर जांच करें।
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If (x=2), what is the left side of \(x^2-5x+6=0\)?
A. (0)
Substitution gives \(2^2-5\cdot2+6=0\). So (x=2) is a solution.
The correct answer is A. (0). Substitution gives \(2^2-5\cdot2+6=0\). So (x=2) is a solution.
रखने पर \(2^2-5\cdot2+6=0\) मिलता है। इसलिए (x=2) समीकरण का हल है।
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Which equation is in the standard form \(ax^2+bx+c=0\)?
A. \(x^2+2x+1=0\)
In standard form the right side is (0). Option (A) matches this form.
The correct answer is A. \(x^2+2x+1=0\). In standard form the right side is (0). Option (A) matches this form.
मानक रूप में दाईं ओर (0) होता है। विकल्प (A) इसी रूप में है।
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Which is the standard form of \(x^2=4x+12\)?
A. \(x^2-4x-12=0\)
When terms from the right side move left, their signs change. Thus \(x^2-4x-12=0\) is correct.
The correct answer is A. \(x^2-4x-12=0\). When terms from the right side move left, their signs change. Thus \(x^2-4x-12=0\) is correct.
दाईं ओर के पदों को बाईं ओर लाने पर चिन्ह बदलते हैं। इसलिए \(x^2-4x-12=0\) सही है।
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What is the standard form of \(2x^2+5x=3\)?
B. \(2x^2+5x-3=0\)
Bringing all terms to one side gives \(2x^2+5x-3=0\). Do not forget the sign change.
The correct answer is B. \(2x^2+5x-3=0\). Bringing all terms to one side gives \(2x^2+5x-3=0\). Do not forget the sign change.
सभी पद एक तरफ लाने पर \(2x^2+5x-3=0\) मिलता है। चिन्ह बदलना न भूलें।
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Under which condition is \(ax^2+bx+c=0\) called a quadratic equation?
B. \(a\neq0\)
The quadratic term must remain, so \(a\neq0\). If (a=0), it may become linear.
The correct answer is B. \(a\neq0\). The quadratic term must remain, so \(a\neq0\). If (a=0), it may become linear.
द्विघात पद बना रहे इसलिए \(a\neq0\) होना चाहिए। परीक्षा में (a=0) होने पर यह रैखिक बन सकता है।
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What is the value of (b) in \(9x^2+11=0\)?
C. (0)
It is written as \(9x^2+0x+11=0\). So (b=0).
The correct answer is C. (0). It is written as \(9x^2+0x+11=0\). So (b=0).
इसे \(9x^2+0x+11=0\) लिखा जाता है। इसलिए (b=0) है।
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What is the value of (c) in \(x^2-6x=0\)?
C. (0)
It can be written as \(x^2-6x+0=0\). Hence (c=0).
The correct answer is C. (0). It can be written as \(x^2-6x+0=0\). Hence (c=0).
इसे \(x^2-6x+0=0\) लिखा जा सकता है। अतः (c=0) है।
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What is the value of (c) in \(4x^2-8x+1=0\)?
C. (1)
In standard form, (c) is the constant term. Here the constant term is (1).
The correct answer is C. (1). In standard form, (c) is the constant term. Here the constant term is (1).
मानक रूप में (c) स्थिर पद होता है। यहां स्थिर पद (1) है।
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What is the value of (b) in \(3x^2+7x-4=0\)?
B. (7)
In standard form, (b) is the coefficient of (x). So (b=7).
The correct answer is B. (7). In standard form, (b) is the coefficient of (x). So (b=7).
मानक रूप में (b) (x) का गुणांक होता है। इसलिए (b=7) है।
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What is the value of (a) in the equation \(5x^2-2x+9=0\)?
A. (5)
In \(ax^2+bx+c=0\), (a) is the coefficient of \(x^2\). Here (a=5).
The correct answer is A. (5). In \(ax^2+bx+c=0\), (a) is the coefficient of \(x^2\). Here (a=5).
मानक रूप \(ax^2+bx+c=0\) में (a) \(x^2\) का गुणांक होता है। यहां (a=5) है।
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Which of the following equations is a quadratic equation?
A. \(x^2+3x+2=0\)
A quadratic equation has highest power (2) of (x). In exams first check the degree.
The correct answer is A. \(x^2+3x+2=0\). A quadratic equation has highest power (2) of (x). In exams first check the degree.
द्विघात समीकरण में (x) की सबसे बड़ी घात (2) होती है। परीक्षा में सबसे पहले घात देखें।
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