32 results found for "verification" in Class 10.
Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(8x^2-14x-15=0\) को हल करने में कौनसा गुणनखंड रूप सही है?
Which factorised form is correct for solving \(8x^2-14x-15=0\)?
#quadratic
#factorisation
#verification
A ((4x+3)(2x-5)=0)
B ((4x-3)(2x+5)=0)
C ((8x+5)(x-3)=0)
D ((x+5)(8x-3)=0)
Explanation opens after your attempt
Correct Answer
A. ((4x+3)(2x-5)=0)
Step 1
Concept
((4x+3)(2x-5)=8x-2 -20x+6x-15=8x-2 -14x-15), so it is correct. In exams, verify factorisation by expanding.
Step 2
Why this answer is correct
The correct answer is A. ((4x+3)(2x-5)=0). ((4x+3)(2x-5)=8x-2 -20x+6x-15=8x-2 -14x-15), so it is correct. In exams, verify factorisation by expanding.
Step 3
Exam Tip
((4x+3)(2x-5)=8x-2 -20x+6x-15=8x-2 -14x-15), इसलिए यह सही है। परीक्षा में गुणनखंड को विस्तार करके जांचें।
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Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(7x^2-19x-6=0\) को हल करने में कौनसा गुणनखंड रूप सही है?
Which factorised form is correct for solving \(7x^2-19x-6=0\)?
#quadratic
#factorisation
#verification
A ((7x+2)(x-3)=0)
B ((7x-2)(x+3)=0)
C ((x+2)(7x-3)=0)
D ((7x-3)(x+2)=0)
Explanation opens after your attempt
Correct Answer
A. ((7x+2)(x-3)=0)
Step 1
Concept
((7x+2)(x-3)=7x-2 -19x-6), so it is correct. In exams, verify factorisation by expanding.
Step 2
Why this answer is correct
The correct answer is A. ((7x+2)(x-3)=0). ((7x+2)(x-3)=7x-2 -19x-6), so it is correct. In exams, verify factorisation by expanding.
Step 3
Exam Tip
((7x+2)(x-3)=7x-2 -19x-6), इसलिए यह सही है। परीक्षा में गुणनखंड को विस्तार करके जांचें।
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Question
Expert Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(6x^2-11x-10=0\) को हल करने में कौनसा गुणनखंड रूप सही है?
Which factorised form is correct for solving \(6x^2-11x-10=0\)?
#quadratic
#factorisation
#verification
A ((3x+2)(2x-5)=0)
B ((3x-2)(2x+5)=0)
C ((6x+5)(x-2)=0)
D ((2x+5)(3x-2)=0)
Explanation opens after your attempt
Correct Answer
A. ((3x+2)(2x-5)=0)
Step 1
Concept
((3x+2)(2x-5)=6x-2 -11x-10), so it is correct. In exams, verify factorisation by expanding.
Step 2
Why this answer is correct
The correct answer is A. ((3x+2)(2x-5)=0). ((3x+2)(2x-5)=6x-2 -11x-10), so it is correct. In exams, verify factorisation by expanding.
Step 3
Exam Tip
((3x+2)(2x-5)=6x-2 -11x-10), इसलिए यह सही है। परीक्षा में गुणनखंड को विस्तार करके जांचें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(5x^2-7x-6=0\) को हल करने में कौनसा गुणनखंड रूप सही है?
Which factorised form is correct for solving \(5x^2-7x-6=0\)?
#quadratic
#factorisation
#verification
A ((5x+3)(x-2)=0)
B ((5x-3)(x+2)=0)
C ((x+3)(5x-2)=0)
D ((5x-2)(x+3)=0)
Explanation opens after your attempt
Correct Answer
A. ((5x+3)(x-2)=0)
Step 1
Concept
((5x+3)(x-2)=5x-2 -7x-6), so it is correct. In exams, verify factorisation by expanding.
Step 2
Why this answer is correct
The correct answer is A. ((5x+3)(x-2)=0). ((5x+3)(x-2)=5x-2 -7x-6), so it is correct. In exams, verify factorisation by expanding.
Step 3
Exam Tip
((5x+3)(x-2)=5x-2 -7x-6), इसलिए यह सही है। परीक्षा में गुणनखंड को विस्तार करके जांचें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(3x^2-5x-2=0\) को हल करने में कौनसा गुणनखंड रूप सही है?
Which factorised form is correct for solving \(3x^2-5x-2=0\)?
#quadratic
#factorisation
#verification
A ((3x+1)(x-2)=0)
B ((3x-1)(x+2)=0)
C ((x+1)(3x-2)=0)
D ((3x-2)(x+1)=0)
Explanation opens after your attempt
Correct Answer
A. ((3x+1)(x-2)=0)
Step 1
Concept
((3x+1)(x-2)=3x-2 -5x-2), so it is correct. In exams, verify factorisation by expanding.
Step 2
Why this answer is correct
The correct answer is A. ((3x+1)(x-2)=0). ((3x+1)(x-2)=3x-2 -5x-2), so it is correct. In exams, verify factorisation by expanding.
Step 3
Exam Tip
((3x+1)(x-2)=3x-2 -5x-2), इसलिए यह सही है। परीक्षा में गुणनखंड को विस्तार करके जांचें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(5x^2-18x+9=0\) के मूल क्या होंगे?
What will be the roots of \(5x^2-18x+9=0\)?
#quadratic
#roots
#verification
A \(x=3,\frac{3}{5}\)
B \(x=-3,-\frac{3}{5}\)
C \(x=\frac{5}{3},3\)
D \(x=1,\frac{9}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(x=3,\frac{3}{5}\)
Step 1
Concept
(5x-2 -18x+9=(5x-3)(x-3)), so the roots are \(\frac{3}{5}\) and (3). In exams, verify the answer quickly by factorisation.
Step 2
Why this answer is correct
The correct answer is A. \(x=3,\frac{3}{5}\). (5x-2 -18x+9=(5x-3)(x-3)), so the roots are \(\frac{3}{5}\) and (3). In exams, verify the answer quickly by factorisation.
Step 3
Exam Tip
(5x-2 -18x+9=(5x-3)(x-3)), इसलिए मूल \(\frac{3}{5}\) और (3) हैं। परीक्षा में गुणनखंड विधि से उत्तर जल्दी जांचें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(2x^2-3x-2=0\) को हल करने में कौनसा गुणनखंड रूप सही है?
Which factorised form is correct for solving \(2x^2-3x-2=0\)?
#quadratic
#factorisation
#verification
A ((2x+1)(x-2)=0)
B ((2x-1)(x+2)=0)
C ((x+1)(2x-2)=0)
D ((2x-2)(x+1)=0)
Explanation opens after your attempt
Correct Answer
A. ((2x+1)(x-2)=0)
Step 1
Concept
((2x+1)(x-2)=2x-2 -3x-2), so it is correct. In exams, verify the factorisation by expanding.
Step 2
Why this answer is correct
The correct answer is A. ((2x+1)(x-2)=0). ((2x+1)(x-2)=2x-2 -3x-2), so it is correct. In exams, verify the factorisation by expanding.
Step 3
Exam Tip
((2x+1)(x-2)=2x-2 -3x-2), इसलिए यह सही है। परीक्षा में गुणनखंड को विस्तार करके जांचें।
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Question
Hard Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(3x^2-10x+3=0\) के मूल क्या होंगे?
What will be the roots of \(3x^2-10x+3=0\)?
#quadratic
#roots
#verification
A \(x=3,\frac{1}{3}\)
B \(x=-3,-\frac{1}{3}\)
C \(x=\frac{3}{2},2\)
D \(x=1,\frac{10}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(x=3,\frac{1}{3}\)
Step 1
Concept
(3x-2 -10x+3=(3x-1)(x-3)), so the roots are \(\frac{1}{3}\) and (3). In exams, you may verify by completing square or factoring.
Step 2
Why this answer is correct
The correct answer is A. \(x=3,\frac{1}{3}\). (3x-2 -10x+3=(3x-1)(x-3)), so the roots are \(\frac{1}{3}\) and (3). In exams, you may verify by completing square or factoring.
Step 3
Exam Tip
(3x-2 -10x+3=(3x-1)(x-3)), इसलिए मूल \(\frac{1}{3}\) और (3) हैं। परीक्षा में पूर्ण वर्ग या गुणनखंड दोनों से जांच सकते हैं।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(4x^2-12x-7=0\) में कौनसा गुणनखंड रूप सही है?
Which factorised form is correct for \(4x^2-12x-7=0\)?
#quadratic
#factorisation
#verification
A ((2x+1)(2x-7)=0)
B ((2x-1)(2x+7)=0)
C ((4x-7)(x+1)=0)
D ((x+7)(4x-1)=0)
Explanation opens after your attempt
Correct Answer
A. ((2x+1)(2x-7)=0)
Step 1
Concept
((2x+1)(2x-7)=4x-2 -12x-7), so this is the correct factorised form. In exams, check the answer by expanding.
Step 2
Why this answer is correct
The correct answer is A. ((2x+1)(2x-7)=0). ((2x+1)(2x-7)=4x-2 -12x-7), so this is the correct factorised form. In exams, check the answer by expanding.
Step 3
Exam Tip
((2x+1)(2x-7)=4x-2 -12x-7), इसलिए यह सही गुणनखंड रूप है। परीक्षा में विस्तार करके उत्तर जांचें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 36
\(11x^2+12x+1=0\) में कौनसा गुणनखंड रूप सही है?
Which factorised form is correct for \(11x^2+12x+1=0\)?
#quadratic
#factorisation
#verification
A ((11x+1)(x+1)=0)
B ((11x-1)(x-1)=0)
C ((x+11)(x+1)=0)
D ((11x+12)(x+1)=0)
Explanation opens after your attempt
Correct Answer
A. ((11x+1)(x+1)=0)
Step 1
Concept
((11x+1)(x+1)=11x-2 +12x+1), so it is correct. In exams, verify the factors by expanding.
Step 2
Why this answer is correct
The correct answer is A. ((11x+1)(x+1)=0). ((11x+1)(x+1)=11x-2 +12x+1), so it is correct. In exams, verify the factors by expanding.
Step 3
Exam Tip
((11x+1)(x+1)=11x-2 +12x+1), इसलिए यह सही है। परीक्षा में गुणनखंड को विस्तार करके जांचें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(3x^2-10x-8=0\) में कौनसा गुणनखंड रूप सही है?
Which factorised form is correct for \(3x^2-10x-8=0\)?
#quadratic
#factorisation
#verification
A ((3x+2)(x-4)=0)
B ((3x-2)(x+4)=0)
C ((3x-4)(x+2)=0)
D ((x+4)(x-8)=0)
Explanation opens after your attempt
Correct Answer
A. ((3x+2)(x-4)=0)
Step 1
Concept
((3x+2)(x-4)=3x-2 -10x-8), so this is the correct factorised form. In exams, check the answer by expanding.
Step 2
Why this answer is correct
The correct answer is A. ((3x+2)(x-4)=0). ((3x+2)(x-4)=3x-2 -10x-8), so this is the correct factorised form. In exams, check the answer by expanding.
Step 3
Exam Tip
((3x+2)(x-4)=3x-2 -10x-8), इसलिए यह सही गुणनखंड रूप है। परीक्षा में विस्तार करके उत्तर जांचें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 35
\(7x^2+8x+1=0\) में कौनसा गुणनखंड रूप सही है?
Which factorised form is correct for \(7x^2+8x+1=0\)?
#quadratic
#factorisation
#verification
A ((7x+1)(x+1)=0)
B ((7x-1)(x-1)=0)
C ((x+7)(x+1)=0)
D ((7x+8)(x+1)=0)
Explanation opens after your attempt
Correct Answer
A. ((7x+1)(x+1)=0)
Step 1
Concept
((7x+1)(x+1)=7x-2 +8x+1), so it is correct. In exams, verify the factors by expanding.
Step 2
Why this answer is correct
The correct answer is A. ((7x+1)(x+1)=0). ((7x+1)(x+1)=7x-2 +8x+1), so it is correct. In exams, verify the factors by expanding.
Step 3
Exam Tip
((7x+1)(x+1)=7x-2 +8x+1), इसलिए यह सही है। परीक्षा में गुणनखंड को विस्तार करके जांचें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(2x^2-3x-2=0\) में कौनसा गुणनखंड रूप सही है?
Which factorised form is correct for \(2x^2-3x-2=0\)?
#quadratic
#factorisation
#verification
A ((2x+1)(x-2)=0)
B ((2x-1)(x+2)=0)
C ((2x-2)(x+1)=0)
D ((x+2)(x-2)=0)
Explanation opens after your attempt
Correct Answer
A. ((2x+1)(x-2)=0)
Step 1
Concept
((2x+1)(x-2)=2x-2 -3x-2), so this is the correct factorised form. In exams, check the answer by expanding.
Step 2
Why this answer is correct
The correct answer is A. ((2x+1)(x-2)=0). ((2x+1)(x-2)=2x-2 -3x-2), so this is the correct factorised form. In exams, check the answer by expanding.
Step 3
Exam Tip
((2x+1)(x-2)=2x-2 -3x-2), इसलिए यह सही गुणनखंड रूप है। परीक्षा में विस्तार करके उत्तर जांचें।
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Question
Medium Mathematics
Quadratic Equations Methods of Solving Quadratic Equations Class 10 Level 34
\(5x^2+6x+1=0\) में कौनसा गुणनखंड रूप सही है?
Which factorised form is correct for \(5x^2+6x+1=0\)?
#quadratic
#factorisation
#verification
A ((5x+1)(x+1)=0)
B ((5x-1)(x-1)=0)
C ((x+5)(x+1)=0)
D ((5x+6)(x+1)=0)
Explanation opens after your attempt
Correct Answer
A. ((5x+1)(x+1)=0)
Step 1
Concept
((5x+1)(x+1)=5x-2 +6x+1), so it is correct. In exams, verify factors by expanding.
Step 2
Why this answer is correct
The correct answer is A. ((5x+1)(x+1)=0). ((5x+1)(x+1)=5x-2 +6x+1), so it is correct. In exams, verify factors by expanding.
Step 3
Exam Tip
((5x+1)(x+1)=5x-2 +6x+1), इसलिए यह सही है। परीक्षा में विस्तार करके गुणनखंड जांचें।
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Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि (4x-2 -(5t+3)x+t(t+3)=0) की जड़ें (t) और \(\frac{t+3}{4}\) बताई गई हैं, तो यह कथन कब सत्य है?
If the roots of (4x-2 -(5t+3)x+t(t+3)=0) are said to be (t) and \(\frac{t+3}{4}\), when is this statement true?
#quadratic-roots
#parametric-roots
#verification
A हर (t) के लिए / For every (t)
B केवल (t=0) पर / Only at (t=0)
C केवल (t=3) पर / Only at (t=3)
D कभी नहीं / Never
Explanation opens after your attempt
Correct Answer
A. हर (t) के लिए / For every (t)
Step 1
Concept
The sum of these roots is \(\frac{5t+3}{4}\), and the product is (\frac{t(t+3)}{4}). These match \(-\frac{b}{a}\) and \(\frac{c}{a}\) of the given equation.
Step 2
Why this answer is correct
The correct answer is A. हर (t) के लिए / For every (t). The sum of these roots is \(\frac{5t+3}{4}\), and the product is (\frac{t(t+3)}{4}). These match \(-\frac{b}{a}\) and \(\frac{c}{a}\) of the given equation.
Step 3
Exam Tip
इन जड़ों का योग \(\frac{5t+3}{4}\) और गुणनफल (\frac{t(t+3)}{4}) है। ये दिए गए समीकरण के \(-\frac{b}{a}\) और \(\frac{c}{a}\) से मेल खाते हैं।
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Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
(x-2 -(a+8)x+8a=0) के बारे में कौन-सा कथन हमेशा सही है?
Which statement is always correct about (x-2 -(a+8)x+8a=0)?
#quadratic-roots
#parametric-equation
#root-verification
A (8) हमेशा एक जड़ है / (8) is always one root
B (a+8) हमेशा एक जड़ है / (a+8) is always one root
C दोनों जड़ें हमेशा (8) हैं / Both roots are always (8)
D जड़ें कभी वास्तविक नहीं हैं / The roots are never real
Explanation opens after your attempt
Correct Answer
A. (8) हमेशा एक जड़ है / (8) is always one root
Step 1
Concept
Putting (x=8) gives (64-8(a+8)+8a=0). Hence (8) is always one root and the other root is (a).
Step 2
Why this answer is correct
The correct answer is A. (8) हमेशा एक जड़ है / (8) is always one root. Putting (x=8) gives (64-8(a+8)+8a=0). Hence (8) is always one root and the other root is (a).
Step 3
Exam Tip
(x=8) रखने पर (64-8(a+8)+8a=0) मिलता है। इसलिए (8) हमेशा एक जड़ है और दूसरी जड़ (a) है।
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Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि (3x-2 -(4t+2)x+t(t+2)=0) की जड़ें (t) और \(\frac{t+2}{3}\) बताई गई हैं, तो यह कथन कब सत्य है?
If the roots of (3x-2 -(4t+2)x+t(t+2)=0) are said to be (t) and \(\frac{t+2}{3}\), when is this statement true?
#quadratic-roots
#parametric-roots
#verification
A केवल (t=0) पर / Only at (t=0)
B केवल (t=1) पर / Only at (t=1)
C हर (t) पर / For every (t)
D कभी नहीं / Never
Explanation opens after your attempt
Correct Answer
C. हर (t) पर / For every (t)
Step 1
Concept
The sum of these two roots is \(\frac{4t+2}{3}\), and the product is (\frac{t(t+2)}{3}). These match \(-\frac{b}{a}\) and \(\frac{c}{a}\) of the given equation.
Step 2
Why this answer is correct
The correct answer is C. हर (t) पर / For every (t). The sum of these two roots is \(\frac{4t+2}{3}\), and the product is (\frac{t(t+2)}{3}). These match \(-\frac{b}{a}\) and \(\frac{c}{a}\) of the given equation.
Step 3
Exam Tip
इन दोनों जड़ों का योग \(\frac{4t+2}{3}\) और गुणनफल (\frac{t(t+2)}{3}) है। ये दिए गए समीकरण के \(-\frac{b}{a}\) और \(\frac{c}{a}\) से मेल खाते हैं।
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Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
(x-2 -(a+6)x+6a=0) के लिए कौन-सा कथन हमेशा सत्य है?
Which statement is always true for (x-2 -(a+6)x+6a=0)?
#quadratic-roots
#root-verification
#parametric-equation
A (a+6) हमेशा जड़ है / (a+6) is always a root
B (6) हमेशा जड़ है / (6) is always a root
C दोनों जड़ें हमेशा समान हैं / Both roots are always equal
D जड़ें कभी वास्तविक नहीं हैं / The roots are never real
Explanation opens after your attempt
Correct Answer
B. (6) हमेशा जड़ है / (6) is always a root
Step 1
Concept
Putting (x=6) gives (36-6(a+6)+6a=0). Hence (6) is always one root and the other root is (a).
Step 2
Why this answer is correct
The correct answer is B. (6) हमेशा जड़ है / (6) is always a root. Putting (x=6) gives (36-6(a+6)+6a=0). Hence (6) is always one root and the other root is (a).
Step 3
Exam Tip
(x=6) रखने पर (36-6(a+6)+6a=0) मिलता है। इसलिए (6) हमेशा एक जड़ है और दूसरी जड़ (a) है।
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Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि (2x-2 -(3t+1)x+t-2 +t=0) की जड़ें (t) और \(\frac{t+1}{2}\) हैं, तो यह कथन किसके लिए सही है?
If the roots of (2x-2 -(3t+1)x+t-2 +t=0) are (t) and \(\frac{t+1}{2}\), for which values is this statement true?
#quadratic-roots
#verification
#parametric-roots
A हर (t) के लिए / For every (t)
B केवल (t=1) के लिए / Only for (t=1)
C केवल (t=0) के लिए / Only for (t=0)
D किसी भी (t) के लिए नहीं / For no (t)
Explanation opens after your attempt
Correct Answer
A. हर (t) के लिए / For every (t)
Step 1
Concept
The sum is \(\frac{3t+1}{2}\) and the product is (\frac{t(t+1)}{2}). These match \(-\frac{b}{a}\) and \(\frac{c}{a}\) for every (t).
Step 2
Why this answer is correct
The correct answer is A. हर (t) के लिए / For every (t). The sum is \(\frac{3t+1}{2}\) and the product is (\frac{t(t+1)}{2}). These match \(-\frac{b}{a}\) and \(\frac{c}{a}\) for every (t).
Step 3
Exam Tip
इन जड़ों का योग \(\frac{3t+1}{2}\) और गुणनफल (\frac{t(t+1)}{2}) है। ये दिए गए समीकरण के \(-\frac{b}{a}\) और \(\frac{c}{a}\) से हर (t) पर मेल खाते हैं।
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Question
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
(x-2 -(a+4)x+4a=0) के लिए कौन-सा कथन हमेशा सत्य है?
Which statement is always true for (x-2 -(a+4)x+4a=0)?
#quadratic-roots
#root-verification
#identity
A (4) हमेशा एक जड़ है / (4) is always a root
B (a+4) हमेशा एक जड़ है / (a+4) is always a root
C दोनों जड़ें हमेशा समान हैं / Both roots are always equal
D जड़ें कभी वास्तविक नहीं हैं / The roots are never real
Explanation opens after your attempt
Correct Answer
A. (4) हमेशा एक जड़ है / (4) is always a root
Step 1
Concept
Putting (x=4) gives (16-4(a+4)+4a=0). Hence (4) is always one root and the other root is (a).
Step 2
Why this answer is correct
The correct answer is A. (4) हमेशा एक जड़ है / (4) is always a root. Putting (x=4) gives (16-4(a+4)+4a=0). Hence (4) is always one root and the other root is (a).
Step 3
Exam Tip
(x=4) रखने पर (16-4(a+4)+4a=0) मिलता है। अतः (4) हमेशा एक जड़ है और दूसरी जड़ (a) होती है।
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Question
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि (x=0), \(ax^2+bx+c=0\) की जड़ है, तो कौन-सी शर्त निश्चित रूप से सही है?
If (x=0) is a root of \(ax^2+bx+c=0\), which condition must be true?
#quadratic-roots
#zero-root
#root-verification
A (c=0)
B (b=0)
C (a=0)
D (a+b=0)
Explanation opens after your attempt
Step 1
Concept
Putting (x=0) gives (c=0). Thus the direct condition for zero to be a root is (c=0).
Step 2
Why this answer is correct
The correct answer is A. (c=0). Putting (x=0) gives (c=0). Thus the direct condition for zero to be a root is (c=0).
Step 3
Exam Tip
(x=0) रखने पर समीकरण (c=0) बनता है। इसलिए शून्य जड़ होने की सीधी शर्त (c=0) है।
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Question
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
(x-2 -(a+3)x+3a=0) के बारे में कौन-सा कथन हमेशा सही है?
Which statement is always true about (x-2 -(a+3)x+3a=0)?
#quadratic-roots
#root-verification
#parameter
A (3) हमेशा एक जड़ है / (3) is always a root
B (a) कभी जड़ नहीं है / (a) is never a root
C दोनों जड़ें हमेशा समान हैं / Both roots are always equal
D कोई वास्तविक जड़ नहीं है / There is no real root
Explanation opens after your attempt
Correct Answer
A. (3) हमेशा एक जड़ है / (3) is always a root
Step 1
Concept
Putting (x=3) gives (9-3(a+3)+3a=0). Hence (3) is always one root, and the other root is (a).
Step 2
Why this answer is correct
The correct answer is A. (3) हमेशा एक जड़ है / (3) is always a root. Putting (x=3) gives (9-3(a+3)+3a=0). Hence (3) is always one root, and the other root is (a).
Step 3
Exam Tip
(x=3) रखने पर (9-3(a+3)+3a=0) मिलता है। इसलिए (3) हमेशा एक जड़ है और दूसरी जड़ (a) होती है।
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Question
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि (x=2), \(kx^2-6x+4=0\) की जड़ है, तो (k) का मान क्या है?
If (x=2) is a root of \(kx^2-6x+4=0\), what is (k)?
#quadratic-roots
#root-verification
#parameter
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
Putting (x=2), we get (4k-12+4=0). Hence (4k=8) and (k=2).
Step 2
Why this answer is correct
The correct answer is B. (2). Putting (x=2), we get (4k-12+4=0). Hence (4k=8) and (k=2).
Step 3
Exam Tip
(x=2) रखने पर (4k-12+4=0) मिलता है। इसलिए (4k=8) और (k=2)।
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Question
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2-15x+56=0\), तो (x=7) रखने पर बायां पक्ष क्या बनेगा?
If \(x^2-15x+56=0\), what will the left side become when (x=7)?
#quadratic-equations
#substitution
#root-verification
#medium
A (0)
B (7)
C (-7)
D (14)
Explanation opens after your attempt
Step 1
Concept
\(7^2-15\cdot7+56=49-105+56=0\). If the left side becomes (0), the given value is a root.
Step 2
Why this answer is correct
The correct answer is A. (0). \(7^2-15\cdot7+56=49-105+56=0\). If the left side becomes (0), the given value is a root.
Step 3
Exam Tip
\(7^2-15\cdot7+56=49-105+56=0\) है। बायां पक्ष (0) हो तो दिया मान मूल है।
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Question
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2-12x+35=0\), तो (x=5) रखने पर बायां पक्ष क्या बनेगा?
If \(x^2-12x+35=0\), what will the left side become when (x=5)?
#quadratic-equations
#substitution
#root-verification
#medium
A (0)
B (5)
C (-5)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(5^2-12\cdot5+35=25-60+35=0\). If the left side becomes (0), the given value is a root.
Step 2
Why this answer is correct
The correct answer is A. (0). \(5^2-12\cdot5+35=25-60+35=0\). If the left side becomes (0), the given value is a root.
Step 3
Exam Tip
\(5^2-12\cdot5+35=25-60+35=0\) है। बायां पक्ष (0) हो तो दिया मान मूल है।
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Question
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि \(x^2-9x+20=0\), तो (x=4) रखने पर बायां पक्ष क्या बनेगा?
If \(x^2-9x+20=0\), what will the left side become when (x=4)?
#quadratic-equations
#substitution
#root-verification
#medium
A (0)
B (4)
C (-4)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(4^2-9\cdot4+20=16-36+20=0\). If the left side becomes (0), the given value is a root.
Step 2
Why this answer is correct
The correct answer is A. (0). \(4^2-9\cdot4+20=16-36+20=0\). If the left side becomes (0), the given value is a root.
Step 3
Exam Tip
\(4^2-9\cdot4+20=16-36+20=0\) है। यदि बायां पक्ष (0) हो तो दिया मान मूल होता है।
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Question
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
क्या (x=0) समीकरण \(x^2+5x=0\) का मूल है?
Is (x=0) a root of \(x^2+5x=0\)?
#quadratic-equations
#root-verification
#easy
A हाँ / Yes
B नहीं / No
C केवल (x=5) मूल है / Only (x=5) is a root
D केवल (x=-5) मूल है / Only (x=-5) is a root
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Putting (x=0) gives \(0^2+5\cdot0=0\). Substitution is the easiest way to check a root.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Putting (x=0) gives \(0^2+5\cdot0=0\). Substitution is the easiest way to check a root.
Step 3
Exam Tip
(x=0) रखने पर \(0^2+5\cdot0=0\) मिलता है। मूल जांचने में प्रतिस्थापन सबसे आसान तरीका है।
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Question
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
कौन सा विकल्प \(x^2+x-12=0\) का गुणनखंड रूप है?
Which option is the factor form of \(x^2+x-12=0\)?
#quadratic equations
#factor form
#verification
A ((x+4)(x-3)=0)
B ((x-4)(x+3)=0)
C ((x+4)(x+3)=0)
D ((x-4)(x-3)=0)
Explanation opens after your attempt
Correct Answer
A. ((x+4)(x-3)=0)
Step 1
Concept
Expanding ((x+4)(x-3)) gives \(x^2+x-12\). To check factors, expand them.
Step 2
Why this answer is correct
The correct answer is A. ((x+4)(x-3)=0). Expanding ((x+4)(x-3)) gives \(x^2+x-12\). To check factors, expand them.
Step 3
Exam Tip
((x+4)(x-3)) फैलाने पर \(x^2+x-12\) मिलता है। गुणनखंड जांचने के लिए विस्तार करें।
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Question
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
\(x^2+6x+9=0\) में (x=-3) रखने पर क्या होगा?
What happens when (x=-3) is put in \(x^2+6x+9=0\)?
#quadratic equations
#negative root
#verification
A समीकरण संतुष्ट होता है / The equation is satisfied
B समीकरण असत्य होता है / The equation is false
C बायां पक्ष (6) होता है / The left side is (6)
D बायां पक्ष (-6) होता है / The left side is (-6)
Explanation opens after your attempt
Correct Answer
A. समीकरण संतुष्ट होता है / The equation is satisfied
Step 1
Concept
((-3)2 +6(-3)+9=0). Hence (x=-3) is a solution.
Step 2
Why this answer is correct
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.
Step 3
Exam Tip
((-3)2 +6(-3)+9=0) है। अतः (x=-3) हल है।
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Question
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
कौन सा विकल्प \(x^2-2x-15=0\) का गुणनखंड रूप है?
Which option is the factor form of \(x^2-2x-15=0\)?
#quadratic equations
#factor form
#verification
A \((x-5)(x+3)=0\)
B \((x+5)(x-3)=0\)
C \((x-5)(x-3)=0\)
D \((x+5)(x+3)=0\)
Explanation opens after your attempt
Correct Answer
A. \((x-5)(x+3)=0\)
Step 1
Concept
Expanding ((x-5)(x+3)) gives \(x^2-2x-15\). To check factors, expand them.
Step 2
Why this answer is correct
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.
Step 3
Exam Tip
((x-5)(x+3)) फैलाने पर \(x^2-2x-15\) मिलता है। गुणनखंड जांचने के लिए विस्तार करें।
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Question
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
\(x^2+4x+4=0\) में (x=-2) रखने पर क्या होगा?
What happens when (x=-2) is put in \(x^2+4x+4=0\)?
#quadratic equations
#negative root
#verification
A समीकरण संतुष्ट होता है / The equation is satisfied
B समीकरण असत्य होता है / The equation is false
C बायां पक्ष (4) होता है / The left side is (4)
D बायां पक्ष (-4) होता है / The left side is (-4)
Explanation opens after your attempt
Correct Answer
A. समीकरण संतुष्ट होता है / The equation is satisfied
Step 1
Concept
((-2)2 +4(-2)+4=0). Hence (x=-2) is a solution.
Step 2
Why this answer is correct
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.
Step 3
Exam Tip
((-2)2 +4(-2)+4=0) है। अतः (x=-2) हल है।
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Question
Expert Mathematics
Polynomials Irrational numbers and real numbers Class 10 Level 25
यदि (p(x)=x-2 -2x-2), तो \(1+\sqrt{3}\) के बारे में कौन सा कथन सही है?
If (p(x)=x-2 -2x-2), which statement about \(1+\sqrt{3}\) is correct?
#zero-verification
#irrational-number
#polynomial
A यह (p(x)) का शून्यक है / It is a zero of (p(x))
B यह (p(x)) का शून्यक नहीं है / It is not a zero of (p(x))
C यह परिमेय शून्यक है / It is a rational zero
D यह अवास्तविक संख्या है / It is a non-real number
Explanation opens after your attempt
Correct Answer
A. यह (p(x)) का शून्यक है / It is a zero of (p(x))
Step 1
Concept
Since (p\(1+\sqrt{3}\)=0), \(1+\sqrt{3}\) is a zero. To prove a number is a zero, show that the polynomial value is (0).
Step 2
Why this answer is correct
The correct answer is A. यह (p(x)) का शून्यक है / It is a zero of (p(x)). Since (p\(1+\sqrt{3}\)=0), \(1+\sqrt{3}\) is a zero. To prove a number is a zero, show that the polynomial value is (0).
Step 3
Exam Tip
(p\(1+\sqrt{3}\)=0), इसलिए \(1+\sqrt{3}\) शून्यक है। किसी संख्या को शून्यक सिद्ध करने के लिए बहुपद का मान (0) दिखाएँ।
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