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600 questions tagged with quadratic equations.
What is the degree of \(6x^2-5x+2=0\)?
C. (2)
The highest power is (2). Therefore it is a quadratic equation.
The correct answer is C. (2). The highest power is (2). Therefore it is a quadratic equation.
सबसे बड़ी घात (2) है। इसलिए यह द्विघात समीकरण है।
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What is the value of (a-b+c) for \(4x^2-2x-6=0\)?
A. (0)
Here (a=4), (b=-2), (c=-6). Thus (a-b+c=4-(-2)-6=0).
The correct answer is A. (0). Here (a=4), (b=-2), (c=-6). Thus (a-b+c=4-(-2)-6=0).
यहां (a=4), (b=-2), (c=-6) हैं। इसलिए (a-b+c=4-(-2)-6=0) है।
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What is the value of (a+b+c) for \(5x^2+5x+5=0\)?
C. (15)
Here (a=5), (b=5), (c=5). Therefore (a+b+c=15).
The correct answer is C. (15). Here (a=5), (b=5), (c=5). Therefore (a+b+c=15).
यहां (a=5), (b=5), (c=5) हैं। इसलिए (a+b+c=15) है।
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What is the maximum number of real solutions possible for \(2x^2+7x+3=0\)?
B. (2)
A quadratic equation can have at most (2) real solutions. The degree indicates the maximum number of solutions.
The correct answer is B. (2). A quadratic equation can have at most (2) real solutions. The degree indicates the maximum number of solutions.
द्विघात समीकरण के अधिकतम (2) वास्तविक हल हो सकते हैं। घात से अधिकतम हलों का संकेत मिलता है।
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Which equation becomes \(x^2+2x-8=0\) after writing in standard form?
A. \(x^2+2x=8\)
Moving (8) to the left makes it (-8). So we get \(x^2+2x-8=0\).
The correct answer is A. \(x^2+2x=8\). Moving (8) to the left makes it (-8). So we get \(x^2+2x-8=0\).
(8) को बाईं ओर लाने पर (-8) बनता है। इसलिए \(x^2+2x-8=0\) मिलता है।
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If (a=2), (b=0), (c=-18), what is the equation?
A. \(2x^2-18=0\)
Substituting in standard form gives \(2x^2+0x-18=0\). This is written as \(2x^2-18=0\).
The correct answer is A. \(2x^2-18=0\). Substituting in standard form gives \(2x^2+0x-18=0\). This is written as \(2x^2-18=0\).
मानक रूप में रखने पर \(2x^2+0x-18=0\) मिलता है। इसे \(2x^2-18=0\) लिखते हैं।
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Which form represents (a=3), (b=-4), (c=-2)?
A. \(3x^2-4x-2=0\)
Putting the values in \(ax^2+bx+c=0\) gives \(3x^2-4x-2=0\). Watch the sign of (b).
The correct answer is A. \(3x^2-4x-2=0\). Putting the values in \(ax^2+bx+c=0\) gives \(3x^2-4x-2=0\). Watch the sign of (b).
मानक रूप \(ax^2+bx+c=0\) में मान रखने पर \(3x^2-4x-2=0\) मिलता है। (b) का चिन्ह ध्यान रखें।
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What happens when (x=-3) is put in \(x^2+6x+9=0\)?
A. समीकरण संतुष्ट होता हैThe equation is satisfied
((-3)2+6(-3)+9=0). Hence (x=-3) is a solution.
The correct answer is A. समीकरण संतुष्ट होता है / The equation is satisfied. ((-3)2+6(-3)+9=0). Hence (x=-3) is a solution.
((-3)2+6(-3)+9=0) है। अतः (x=-3) हल है।
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Which equation is a pure quadratic equation?
A. \(4x^2-16=0\)
A pure quadratic has no linear (x) term. \(4x^2-16=0\) is such an equation.
The correct answer is A. \(4x^2-16=0\). A pure quadratic has no linear (x) term. \(4x^2-16=0\) is such an equation.
शुद्ध द्विघात में (x) वाला रैखिक पद नहीं होता। \(4x^2-16=0\) ऐसा समीकरण है।
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Which term is absent in \(x^2-13x=0\)?
C. स्थिर पदConstant term
It can be written as \(x^2-13x+0=0\). So the constant term is absent.
The correct answer is C. स्थिर पद / Constant term. It can be written as \(x^2-13x+0=0\). So the constant term is absent.
इसे \(x^2-13x+0=0\) लिखा जा सकता है। इसलिए स्थिर पद अनुपस्थित है।
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Which option is the constant term in \(6x^2+x-8=0\)?
C. (-8)
The constant term has no variable. Here the constant term is (-8).
The correct answer is C. (-8). The constant term has no variable. Here the constant term is (-8).
स्थिर पद में चर नहीं होता। यहां स्थिर पद (-8) है।
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If (p(x)=x-2-4), what is (p(2))?
A. (0)
(p(2)=22-4=0). So (2) is a zero of this polynomial.
The correct answer is A. (0). (p(2)=22-4=0). So (2) is a zero of this polynomial.
(p(2)=22-4=0) है। इसलिए (2) इस बहुपद का शून्यक है।
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What is the standard form of (4x(x-3)=0)?
A. \(4x^2-12x=0\)
Multiplying (4x) by both terms gives \(4x^2-12x=0\). Pay attention to the negative sign.
The correct answer is A. \(4x^2-12x=0\). Multiplying (4x) by both terms gives \(4x^2-12x=0\). Pay attention to the negative sign.
(4x) को दोनों पदों से गुणा करने पर \(4x^2-12x=0\) मिलता है। ऋण चिन्ह पर ध्यान दें।
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Which equation is quadratic in (t)?
A. \(t^2+3t+2=0\)
In option (A), the variable (t) has highest power (2). So it is quadratic in (t).
The correct answer is A. \(t^2+3t+2=0\). In option (A), the variable (t) has highest power (2). So it is quadratic in (t).
विकल्प (A) में चर (t) की सबसे बड़ी घात (2) है। इसलिए यह (t) में द्विघात है।
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What are (a), (b), (c) in \(3x^2-21=0\)?
A. (3,0,-21)
Write it as \(3x^2+0x-21=0\). So (a=3), (b=0), (c=-21).
The correct answer is A. (3,0,-21). Write it as \(3x^2+0x-21=0\). So (a=3), (b=0), (c=-21).
इसे \(3x^2+0x-21=0\) लिखें। इसलिए (a=3), (b=0), (c=-21) हैं।
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If (x=2), what is the left side of \(x^2+5x-14=0\)?
A. (0)
Substituting gives \(2^2+5\cdot2-14=0\). So (2) is a solution.
The correct answer is A. (0). Substituting gives \(2^2+5\cdot2-14=0\). So (2) is a solution.
रखने पर \(2^2+5\cdot2-14=0\) मिलता है। इसलिए (2) एक हल है।
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How do we write \(x^2-49=0\) in factor form?
A. ((x-7)(x+7)=0)
\(x^2-49\) is a difference of squares. Hence it becomes ((x-7)(x+7)).
The correct answer is A. ((x-7)(x+7)=0). \(x^2-49\) is a difference of squares. Hence it becomes ((x-7)(x+7)).
\(x^2-49\) वर्गों का अंतर है। इसलिए यह ((x-7)(x+7)) बनता है।
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Which equation is equivalent to \(x^2-6x+9=0\)?
A. ((x-3)2=0)
((x-3)2=x-2-6x+9). Recognising perfect squares saves time.
The correct answer is A. ((x-3)2=0). ((x-3)2=x-2-6x+9). Recognising perfect squares saves time.
((x-3)2=x-2-6x+9) होता है। पूर्ण वर्ग पहचानने से समय बचता है।
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What is the linear term in \(9x^2+0x+2=0\)?
B. (0x)
The linear term is the term containing (x). Here the linear term is (0x).
The correct answer is B. (0x). The linear term is the term containing (x). Here the linear term is (0x).
रैखिक पद (x) वाला पद होता है। यहां रैखिक पद (0x) है।
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Which of the following clearly contains the \(x^2\) term?
C. \(4x^2+1=0\)
The quadratic term is the term containing \(x^2\). Option (C) has \(4x^2\).
The correct answer is C. \(4x^2+1=0\). The quadratic term is the term containing \(x^2\). Option (C) has \(4x^2\).
द्विघात पद \(x^2\) वाला पद होता है। विकल्प (C) में \(4x^2\) है।
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If the highest power of the variable in an equation is (2), what is it called?
B. द्विघात समीकरणQuadratic equation
When the highest power is (2), the equation is called quadratic. Identifying degree is the first step.
The correct answer is B. द्विघात समीकरण / Quadratic equation. When the highest power is (2), the equation is called quadratic. Identifying degree is the first step.
सबसे बड़ी घात (2) होने पर समीकरण द्विघात कहलाता है। घात पहचानना पहला कदम है।
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Which value is a solution of \(x^2-3x-10=0\)?
C. (5)
Since \(5^2-3\cdot5-10=0\), (x=5) is a solution.
The correct answer is C. (5). Since \(5^2-3\cdot5-10=0\), (x=5) is a solution.
\(5^2-3\cdot5-10=0\) है। इसलिए (x=5) हल है।
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Which option shows \(x^2+10x+25=0\) in factor form?
A. ((x+5)2=0)
\(x^2+10x+25\) is a perfect square. It equals ((x+5)2).
The correct answer is A. ((x+5)2=0). \(x^2+10x+25\) is a perfect square. It equals ((x+5)2).
\(x^2+10x+25\) पूर्ण वर्ग है। यह ((x+5)2) के बराबर है।
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What is the value of (a) in \(-2x^2+5x-1=0\)?
B. (-2)
The coefficient of \(x^2\) is (-2). So in standard form (a=-2).
The correct answer is B. (-2). The coefficient of \(x^2\) is (-2). So in standard form (a=-2).
\(x^2\) का गुणांक (-2) है। इसलिए मानक रूप में (a=-2) है।
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What is the coefficient of \(x^2\) in \(x^2+12x+36=0\)?
B. (1)
When no number is written before \(x^2\), its coefficient is (1). This is often asked.
The correct answer is B. (1). When no number is written before \(x^2\), its coefficient is (1). This is often asked.
जब \(x^2\) के आगे कोई संख्या नहीं लिखी होती तब गुणांक (1) होता है। यह अक्सर पूछी जाने वाली बात है।
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Which is the standard form of ((x-6)(x+2)=0)?
A. \(x^2-4x-12=0\)
Expansion gives \(x^2+2x-6x-12=0\). So \(x^2-4x-12=0\) is correct.
The correct answer is A. \(x^2-4x-12=0\). Expansion gives \(x^2+2x-6x-12=0\). So \(x^2-4x-12=0\) is correct.
विस्तार से \(x^2+2x-6x-12=0\) मिलता है। इसलिए \(x^2-4x-12=0\) सही है।
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What is the expanded form of ((x+4)(x+5)=0)?
A. \(x^2+9x+20=0\)
Expanding gives \(x^2+5x+4x+20=0\). Combining like terms gives \(x^2+9x+20=0\).
The correct answer is A. \(x^2+9x+20=0\). Expanding gives \(x^2+5x+4x+20=0\). Combining like terms gives \(x^2+9x+20=0\).
विस्तार करने पर \(x^2+5x+4x+20=0\) मिलता है। समान पद जोड़कर \(x^2+9x+20=0\) बनता है।
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Write (2x(x+7)=0) in standard form.
A. \(2x^2+14x=0\)
Multiply (2x) by both terms inside the bracket. This gives \(2x^2+14x=0\).
The correct answer is A. \(2x^2+14x=0\). Multiply (2x) by both terms inside the bracket. This gives \(2x^2+14x=0\).
(2x) को कोष्ठक के दोनों पदों से गुणा करें। इससे \(2x^2+14x=0\) मिलता है।
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For \(12x^2=0\), what are (a), (b), (c) respectively?
A. (12,0,0)
It is written as \(12x^2+0x+0=0\). Therefore (a=12), (b=0), (c=0).
The correct answer is A. (12,0,0). It is written as \(12x^2+0x+0=0\). Therefore (a=12), (b=0), (c=0).
इसे \(12x^2+0x+0=0\) लिखा जाता है। इसलिए (a=12), (b=0), (c=0) हैं।
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What do we get by putting (x=4) in \(x^2-8x+16=0\)?
A. (0=0)
We get \(4^2-8\cdot4+16=0\). So (x=4) satisfies the equation.
The correct answer is A. (0=0). We get \(4^2-8\cdot4+16=0\). So (x=4) satisfies the equation.
\(4^2-8\cdot4+16=0\) मिलता है। इसलिए (x=4) समीकरण को संतुष्ट करता है।
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