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quadratic equations se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
600 questions tagged with quadratic equations.
Which value is one solution of \(x^2-25=0\)?
B. (5)
Since \(5^2-25=0\), (5) is a solution of this equation.
The correct answer is B. (5). Since \(5^2-25=0\), (5) is a solution of this equation.
\(5^2-25=0\) है। इसलिए (5) इस समीकरण का हल है।
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If (x=3), what is the left side of \(x^2-4x+3=0\)?
A. (0)
Substitution gives \(3^2-4\cdot3+3=0\). So (x=3) is a solution.
The correct answer is A. (0). Substitution gives \(3^2-4\cdot3+3=0\). So (x=3) is a solution.
रखने पर \(3^2-4\cdot3+3=0\) मिलता है। इसलिए (x=3) हल है।
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Which is the standard form of \(2x^2=5x+3\)?
A. \(2x^2-5x-3=0\)
Bringing all terms to one side gives \(2x^2-5x-3=0\). Changing signs is important.
The correct answer is A. \(2x^2-5x-3=0\). Bringing all terms to one side gives \(2x^2-5x-3=0\). Changing signs is important.
सभी पद एक तरफ लाने पर \(2x^2-5x-3=0\) मिलता है। चिन्ह बदलना जरूरी है।
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What is the standard form of \(4x^2+7x=9\)?
B. \(4x^2+7x-9=0\)
Moving (9) to the left makes it (-9). So the standard form is \(4x^2+7x-9=0\).
The correct answer is B. \(4x^2+7x-9=0\). Moving (9) to the left makes it (-9). So the standard form is \(4x^2+7x-9=0\).
दाईं ओर के (9) को बाईं ओर लाने पर (-9) बनता है। इसलिए मानक रूप \(4x^2+7x-9=0\) है।
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Under which condition will \(px^2+qx+r=0\) be a quadratic equation?
B. \(p\neq0\)
The quadratic term \(px^2\) must remain, so \(p\neq0\). If (p=0), degree (2) will not remain.
The correct answer is B. \(p\neq0\). The quadratic term \(px^2\) must remain, so \(p\neq0\). If (p=0), degree (2) will not remain.
द्विघात पद \(px^2\) बना रहे इसलिए \(p\neq0\) होना चाहिए। यदि (p=0) हो तो घात (2) नहीं रहेगी।
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What is the value of (b) in \(13x^2-20=0\)?
B. (0)
We write it as \(13x^2+0x-20=0\). So (b=0).
The correct answer is B. (0). We write it as \(13x^2+0x-20=0\). So (b=0).
इसे \(13x^2+0x-20=0\) लिखते हैं। इसलिए (b=0) है।
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What will be the value of (c) in \(11x^2-6x=0\)?
C. (0)
It can be written as \(11x^2-6x+0=0\). So (c=0).
The correct answer is C. (0). It can be written as \(11x^2-6x+0=0\). So (c=0).
इसे \(11x^2-6x+0=0\) लिखा जा सकता है। इसलिए (c=0) है।
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What is the value of (c) in \(8x^2+3x+12=0\)?
C. (12)
In standard form, (c) is the constant term. Here the constant term is (12).
The correct answer is C. (12). In standard form, (c) is the constant term. Here the constant term is (12).
मानक रूप में (c) स्थिर पद होता है। यहां स्थिर पद (12) है।
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What is the value of (b) in \(5x^2-9x+4=0\)?
B. (-9)
In standard form, (b) is the coefficient of (x). Here (b=-9).
The correct answer is B. (-9). In standard form, (b) is the coefficient of (x). Here (b=-9).
मानक रूप में (b) (x) का गुणांक होता है। यहां (b=-9) है।
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What is the value of (a) in \(7x^2+2x-5=0\)?
A. (7)
In \(ax^2+bx+c=0\), (a) is the coefficient of \(x^2\). So (a=7).
The correct answer is A. (7). In \(ax^2+bx+c=0\), (a) is the coefficient of \(x^2\). So (a=7).
मानक रूप \(ax^2+bx+c=0\) में (a) \(x^2\) का गुणांक होता है। इसलिए (a=7) है।
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If \(x^2+kx+12=0\) is a quadratic equation, then (k) is the coefficient of which term?
B. (x) पद(x) term
In \(ax^2+bx+c=0\), (b) is the coefficient of (x). Here in (kx), (k) is the coefficient of (x).
The correct answer is B. (x) पद / (x) term. In \(ax^2+bx+c=0\), (b) is the coefficient of (x). Here in (kx), (k) is the coefficient of (x).
मानक रूप \(ax^2+bx+c=0\) में (x) का गुणांक (b) होता है। यहां (kx) में (k) (x) का गुणांक है।
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Which equation has (x=0) as a solution?
A. \(x^2+5x=0\)
Putting (x=0) in option (A) gives (0=0). Direct substitution is the simplest way to check a solution.
The correct answer is A. \(x^2+5x=0\). Putting (x=0) in option (A) gives (0=0). Direct substitution is the simplest way to check a solution.
(x=0) रखने पर विकल्प (A) में (0=0) मिलता है। हल जांचने का सबसे सरल तरीका प्रत्यक्ष प्रतिस्थापन है।
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Which option shows the common mistake while converting \(x^2=5x-6\) to standard form?
B. \(x^2-5x-6=0\)
The correct form is \(x^2-5x+6=0\). In option (B), the sign of (-6) was not changed.
The correct answer is B. \(x^2-5x-6=0\). The correct form is \(x^2-5x+6=0\). In option (B), the sign of (-6) was not changed.
सही रूप \(x^2-5x+6=0\) है। विकल्प (B) में (-6) का चिन्ह नहीं बदला गया।
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A. (x(x+1)=30)
The next consecutive integer is (x+1). Since the product is (30), the equation is (x(x+1)=30).
The correct answer is A. (x(x+1)=30). The next consecutive integer is (x+1). Since the product is (30), the equation is (x(x+1)=30).
लगातार अगला पूर्णांक (x+1) होगा। गुणनफल (30) है इसलिए (x(x+1)=30) बनेगा।
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If a rectangle has length (x+3) and width (x), and area (10), what equation is formed?
A. (x(x+3)=10)
Area is the product of length and width. So the equation is (x(x+3)=10).
The correct answer is A. (x(x+3)=10). Area is the product of length and width. So the equation is (x(x+3)=10).
क्षेत्रफल लंबाई और चौड़ाई का गुणनफल होता है। इसलिए समीकरण (x(x+3)=10) बनेगा।
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Which option is the factor form of \(x^2-2x-15=0\)?
A. \((x-5)(x+3)=0\)
Expanding ((x-5)(x+3)) gives \(x^2-2x-15\). To check factors, expand them.
The correct answer is A. \((x-5)(x+3)=0\). Expanding ((x-5)(x+3)) gives \(x^2-2x-15\). To check factors, expand them.
((x-5)(x+3)) फैलाने पर \(x^2-2x-15\) मिलता है। गुणनखंड जांचने के लिए विस्तार करें।
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What is the degree of \(5x^2+2x-1=0\)?
C. (2)
The highest power is (2). Therefore the equation is quadratic.
The correct answer is C. (2). The highest power is (2). Therefore the equation is quadratic.
सबसे बड़ी घात (2) है। इसलिए समीकरण द्विघात है।
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What is the value of (a-b+c) for \(2x^2-3x-5=0\)?
A. (0)
Here (a=2), (b=-3), (c=-5). Thus (a-b+c=2-(-3)-5=0).
The correct answer is A. (0). Here (a=2), (b=-3), (c=-5). Thus (a-b+c=2-(-3)-5=0).
यहां (a=2), (b=-3), (c=-5) हैं। इसलिए (a-b+c=2-(-3)-5=0) है।
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What is the value of (a+b+c) for \(4x^2+4x+1=0\)?
C. (9)
Here (a=4), (b=4), (c=1). Therefore (a+b+c=9).
The correct answer is C. (9). Here (a=4), (b=4), (c=1). Therefore (a+b+c=9).
यहां (a=4), (b=4), (c=1) हैं। इसलिए (a+b+c=9) है।
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What is the maximum number of real solutions possible for \(x^2+3x+2=0\)?
B. (2)
A quadratic equation can have at most (2) real solutions. In easy questions, degree indicates the maximum possible solutions.
The correct answer is B. (2). A quadratic equation can have at most (2) real solutions. In easy questions, degree indicates the maximum possible solutions.
द्विघात समीकरण के अधिकतम (2) वास्तविक हल हो सकते हैं। आसान प्रश्न में घात से अधिकतम हल का संकेत मिलता है।
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Which equation becomes \(x^2-7x+10=0\) after writing in standard form?
A. \(x^2-7x=-10\)
In \(x^2-7x=-10\), moving (-10) to the left gives (+10). So the standard form is \(x^2-7x+10=0\).
The correct answer is A. \(x^2-7x=-10\). In \(x^2-7x=-10\), moving (-10) to the left gives (+10). So the standard form is \(x^2-7x+10=0\).
\(x^2-7x=-10\) में (-10) को बाईं ओर लाने पर (+10) बनता है। इसलिए मानक रूप \(x^2-7x+10=0\) है।
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If (a=1), (b=0), (c=-25), what is the equation?
A. \(x^2-25=0\)
Substituting in \(ax^2+bx+c=0\) gives \(x^2+0x-25=0\). This is written as \(x^2-25=0\).
The correct answer is A. \(x^2-25=0\). Substituting in \(ax^2+bx+c=0\) gives \(x^2+0x-25=0\). This is written as \(x^2-25=0\).
\(ax^2+bx+c=0\) में रखने पर \(x^2+0x-25=0\) मिलता है। इसे \(x^2-25=0\) लिखते हैं।
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Which form represents (a=2), (b=-5), (c=3) in \(ax^2+bx+c=0\)?
A. \(2x^2-5x+3=0\)
Putting the given values in standard form gives \(2x^2-5x+3=0\). Keep the sign of (b) carefully.
The correct answer is A. \(2x^2-5x+3=0\). Putting the given values in standard form gives \(2x^2-5x+3=0\). Keep the sign of (b) carefully.
दिए गए मान सीधे मानक रूप में रखने पर \(2x^2-5x+3=0\) मिलता है। (b) का चिन्ह ध्यान रखें।
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What happens when (x=-2) is put in \(x^2+4x+4=0\)?
A. समीकरण संतुष्ट होता हैThe equation is satisfied
((-2)2+4(-2)+4=0). Hence (x=-2) is a solution.
The correct answer is A. समीकरण संतुष्ट होता है / The equation is satisfied. ((-2)2+4(-2)+4=0). Hence (x=-2) is a solution.
((-2)2+4(-2)+4=0) है। अतः (x=-2) हल है।
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Which equation is a pure quadratic like \(x^2+5=0\)?
A. \(x^2-9=0\)
A pure quadratic has no linear (x) term. \(x^2-9=0\) is of that type.
The correct answer is A. \(x^2-9=0\). A pure quadratic has no linear (x) term. \(x^2-9=0\) is of that type.
शुद्ध द्विघात में (x) वाला रैखिक पद नहीं होता। \(x^2-9=0\) ऐसा ही है।
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Which term is absent in \(x^2+10x=0\)?
C. स्थिर पदConstant term
It is treated as \(x^2+10x+0=0\). So the constant term is absent.
The correct answer is C. स्थिर पद / Constant term. It is treated as \(x^2+10x+0=0\). So the constant term is absent.
इसे \(x^2+10x+0=0\) माना जाता है। इसलिए स्थिर पद अनुपस्थित है।
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Which option is the constant term in \(2x^2+3x+1=0\)?
C. (1)
The constant term does not contain (x). Hence (1) is the constant term.
The correct answer is C. (1). The constant term does not contain (x). Hence (1) is the constant term.
स्थिर पद में (x) नहीं होता। इसलिए (1) स्थिर पद है।
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If (p(x)=x-2-1), what is (p(1))?
A. (0)
(p(1)=12-1=0). When (p(a)=0), (a) is called a zero.
The correct answer is A. (0). (p(1)=12-1=0). When (p(a)=0), (a) is called a zero.
(p(1)=12-1=0) है। जब (p(a)=0) हो तो (a) शून्यक कहलाता है।
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What is the standard form of (3x(x-2)=0)?
A. \(3x^2-6x=0\)
Multiplying (3x) by both terms gives \(3x^2-6x=0\). Watch the sign.
The correct answer is A. \(3x^2-6x=0\). Multiplying (3x) by both terms gives \(3x^2-6x=0\). Watch the sign.
(3x) को दोनों पदों से गुणा करने पर \(3x^2-6x=0\) मिलता है। चिन्ह पर ध्यान दें।
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Which equation is quadratic in (x) but not in (y)?
A. \(x^2+5x+6=0\)
In option (A), the variable (x) has degree (2). So it is quadratic in (x).
The correct answer is A. \(x^2+5x+6=0\). In option (A), the variable (x) has degree (2). So it is quadratic in (x).
विकल्प (A) में चर (x) की घात (2) है। इसलिए यह (x) में द्विघात है।
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