\(7x^2+8x+1=0\) 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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\(2x^2-3x-2=0\) 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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\(5x^2+6x+1=0\) 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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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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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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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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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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\(x^2+6x+9=0\) 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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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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\(x^2+4x+4=0\) 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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