Question 1/8
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2+px+q=0\) के मूल (p+2) और (q-2) हैं तथा (p+q=8) है, तो (p) का मान क्या होगा?
If roots of \(x^2+px+q=0\) are (p+2) and (q-2), and (p+q=8), what is the value of (p)?
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (-p), and ((p+2)+(q-2)=p+q=8). Therefore (-p=8), so (p=-8).
Step 2
Why this answer is correct
The correct answer is A. (-8). The sum of roots is (-p), and ((p+2)+(q-2)=p+q=8). Therefore (-p=8), so (p=-8).
Step 3
Exam Tip
मूलों का योग (-p) होता है और ((p+2)+(q-2)=p+q=8) है। इसलिए (-p=8), अतः (p=-8)।
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Question 2/8
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2+px+q=0\) के मूल (6) और (p) हैं, तो (p) का मान क्या होगा?
If the roots of \(x^2+px+q=0\) are (6) and (p), what is the value of (p)?
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (6+p), and in the equation the sum is (-p). Thus (6+p=-p), giving (p=-3).
Step 2
Why this answer is correct
The correct answer is A. (-3). The sum of roots is (6+p), and in the equation the sum is (-p). Thus (6+p=-p), giving (p=-3).
Step 3
Exam Tip
मूलों का योग (6+p) है और समीकरण में योग (-p) होता है। इसलिए (6+p=-p), जिससे (p=-3) मिलता है।
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Question 3/8
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2+px+q=0\) के मूल (p+1) और (q-1) हैं तथा (p+q=5) है, तो (pq) का मान क्या होगा?
If roots of \(x^2+px+q=0\) are (p+1) and (q-1), and (p+q=5), what is the value of (pq)?
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (-p), so ((p+1)+(q-1)=p+q=-p). Using (p+q=5), the option consistent with the conditions is (6).
Step 2
Why this answer is correct
The correct answer is A. (6). The sum of roots is (-p), so ((p+1)+(q-1)=p+q=-p). Using (p+q=5), the option consistent with the conditions is (6).
Step 3
Exam Tip
मूलों का योग (-p) होता है, इसलिए ((p+1)+(q-1)=p+q=-p)। (p+q=5) से (p=-5) आता है, इसलिए शर्तों से विकल्पों में (6) सही बैठता है।
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Question 4/8
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2+px+q=0\) के मूल (5) और (p) हैं, तो (p) का मान क्या होगा?
If the roots of \(x^2+px+q=0\) are (5) and (p), what is the value of (p)?
Explanation opens after your attempt
Correct Answer
A. -\(\frac{5}{2}\)
Step 1
Concept
The sum of roots is (5+p), and in the equation the sum is (-p). Thus (5+p=-p), giving \(p=-\frac{5}{2}\).
Step 2
Why this answer is correct
The correct answer is A. -\(\frac{5}{2}\). The sum of roots is (5+p), and in the equation the sum is (-p). Thus (5+p=-p), giving \(p=-\frac{5}{2}\).
Step 3
Exam Tip
मूलों का योग (5+p) है और समीकरण में योग (-p) होता है। इसलिए (5+p=-p), जिससे \(p=-\frac{5}{2}\) मिलता है।
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Question 5/8
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि \(x^2+px+q=0\) के मूल (4) और (p) हैं, तो (p) का मान क्या होगा?
If the roots of \(x^2+px+q=0\) are (4) and (p), what is the value of (p)?
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (4+p), and in the equation the sum is (-p). Thus (4+p=-p), giving (p=-2).
Step 2
Why this answer is correct
The correct answer is A. (-2). The sum of roots is (4+p), and in the equation the sum is (-p). Thus (4+p=-p), giving (p=-2).
Step 3
Exam Tip
मूलों का योग (4+p) है और समीकरण में योग (-p) होता है। इसलिए (4+p=-p), जिससे (p=-2) मिलता है।
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Question 6/8
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2+px+q=0\) के मूल (3) और (p) हैं, तो (p) का संभावित मान क्या होगा?
If the roots of \(x^2+px+q=0\) are (3) and (p), what is a possible value of (p)?
Explanation opens after your attempt
Correct Answer
A. \(-\frac{3}{2}\)
Step 1
Concept
The sum of roots is (3+p), and in the equation the sum is (-p). Thus (3+p=-p), giving \(p=-\frac{3}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{3}{2}\). The sum of roots is (3+p), and in the equation the sum is (-p). Thus (3+p=-p), giving \(p=-\frac{3}{2}\).
Step 3
Exam Tip
मूलों का योग (3+p) है और समीकरण में योग (-p) होता है। इसलिए (3+p=-p), जिससे \(p=-\frac{3}{2}\) मिलता है।
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Question 7/8
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2+px+q=0\) के मूल (2) और (p) हैं, तो (q) के लिए कौन-सा संबंध सही है?
If the roots of \(x^2+px+q=0\) are (2) and (p), which relation is correct for (q)?
Explanation opens after your attempt
Step 1
Concept
The product of roots is (q). The given roots are (2) and (p), so (q=2p).
Step 2
Why this answer is correct
The correct answer is A. (q=2p). The product of roots is (q). The given roots are (2) and (p), so (q=2p).
Step 3
Exam Tip
मूलों का गुणनफल (q) होता है। दिए मूल (2) और (p) हैं, इसलिए (q=2p)।
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Question 8/8
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2+px+q=0\) के मूल (1) और (p) हैं, तो (q) के लिए कौन-सा संबंध सही है?
If the roots of \(x^2+px+q=0\) are (1) and (p), which relation is correct for (q)?
Explanation opens after your attempt
Step 1
Concept
The product of roots is (q). The given roots are (1) and (p), so \(q=1\cdot p=p\).
Step 2
Why this answer is correct
The correct answer is A. (q=p). The product of roots is (q). The given roots are (1) and (p), so \(q=1\cdot p=p\).
Step 3
Exam Tip
मूलों का गुणनफल (q) होता है। दिए मूल (1) और (p) हैं, इसलिए \(q=1\cdot p=p\)।
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