Question 1/18
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2-8x-33=0\) के मूल \(\alpha,\beta\) हैं, तो \(\alpha\beta+5\alpha+5\beta\) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-8x-33=0\), what is \(\alpha\beta+5\alpha+5\beta\)?
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=8\) and \(\alpha\beta=-33\). Thus (\alpha\beta+5\alpha+5\beta=-33+5(8)=7).
Step 2
Why this answer is correct
The correct answer is A. (7). Here \(\alpha+\beta=8\) and \(\alpha\beta=-33\). Thus (\alpha\beta+5\alpha+5\beta=-33+5(8)=7).
Step 3
Exam Tip
यहाँ \(\alpha+\beta=8\) और \(\alpha\beta=-33\) है। इसलिए (\alpha\beta+5\alpha+5\beta=-33+5(8)=7)।
Login to save your score, XP, coins and progress.
Question 2/18
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2-20x+96=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha-8\)\(\beta-8\)) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-20x+96=0\), what is (\(\alpha-8\)\(\beta-8\))?
Explanation opens after your attempt
Step 1
Concept
(\(\alpha-8\)\(\beta-8\)=\alpha\beta-8\(\alpha+\beta\)+64). Here (96-160+64=0).
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\alpha-8\)\(\beta-8\)=\alpha\beta-8\(\alpha+\beta\)+64). Here (96-160+64=0).
Step 3
Exam Tip
(\(\alpha-8\)\(\beta-8\)=\alpha\beta-8\(\alpha+\beta\)+64) है। यहाँ (96-160+64=0)।
Login to save your score, XP, coins and progress.
Question 3/18
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2-18x+80=0\) के मूल \(\alpha\) और \(\beta\) हैं, तो (\(\alpha-8\)\(\beta-8\)) का मान क्या है?
If \(\alpha\) and \(\beta\) are roots of \(x^2-18x+80=0\), what is (\(\alpha-8\)\(\beta-8\))?
Explanation opens after your attempt
Step 1
Concept
(\(\alpha-8\)\(\beta-8\)=\alpha\beta-8\(\alpha+\beta\)+64). Here (80-144+64=0).
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\alpha-8\)\(\beta-8\)=\alpha\beta-8\(\alpha+\beta\)+64). Here (80-144+64=0).
Step 3
Exam Tip
(\(\alpha-8\)\(\beta-8\)=\alpha\beta-8\(\alpha+\beta\)+64) है। यहाँ (80-144+64=0)।
Login to save your score, XP, coins and progress.
Question 4/18
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2-7x-30=0\) के मूल \(\alpha,\beta\) हैं, तो \(\alpha\beta+4\alpha+4\beta\) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-7x-30=0\), what is \(\alpha\beta+4\alpha+4\beta\)?
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=7\) and \(\alpha\beta=-30\). Thus (\alpha\beta+4\alpha+4\beta=-30+4(7)=-2).
Step 2
Why this answer is correct
The correct answer is A. -(2). Here \(\alpha+\beta=7\) and \(\alpha\beta=-30\). Thus (\alpha\beta+4\alpha+4\beta=-30+4(7)=-2).
Step 3
Exam Tip
यहाँ \(\alpha+\beta=7\) और \(\alpha\beta=-30\) है। इसलिए (\alpha\beta+4\alpha+4\beta=-30+4(7)=-2)।
Login to save your score, XP, coins and progress.
Question 5/18
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2-16x+63=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha-7\)\(\beta-7\)) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-16x+63=0\), what is (\(\alpha-7\)\(\beta-7\))?
Explanation opens after your attempt
Step 1
Concept
(\(\alpha-7\)\(\beta-7\)=\alpha\beta-7\(\alpha+\beta\)+49). Here (63-112+49=0).
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\alpha-7\)\(\beta-7\)=\alpha\beta-7\(\alpha+\beta\)+49). Here (63-112+49=0).
Step 3
Exam Tip
(\(\alpha-7\)\(\beta-7\)=\alpha\beta-7\(\alpha+\beta\)+49) है। यहाँ (63-112+49=0)।
Login to save your score, XP, coins and progress.
Question 6/18
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2-14x+48=0\) के मूल \(\alpha\) और \(\beta\) हैं, तो (\(\alpha-6\)\(\beta-6\)) का मान क्या है?
If \(\alpha\) and \(\beta\) are roots of \(x^2-14x+48=0\), what is (\(\alpha-6\)\(\beta-6\))?
Explanation opens after your attempt
Step 1
Concept
(\(\alpha-6\)\(\beta-6\)=\alpha\beta-6\(\alpha+\beta\)+36). Here (48-84+36=0).
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\alpha-6\)\(\beta-6\)=\alpha\beta-6\(\alpha+\beta\)+36). Here (48-84+36=0).
Step 3
Exam Tip
(\(\alpha-6\)\(\beta-6\)=\alpha\beta-6\(\alpha+\beta\)+36) है। यहाँ (48-84+36=0)।
Login to save your score, XP, coins and progress.
Question 7/18
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि \(x^2-6x-27=0\) के मूल \(\alpha,\beta\) हैं, तो \(\alpha\beta+3\alpha+3\beta\) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-6x-27=0\), what is \(\alpha\beta+3\alpha+3\beta\)?
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=6\) and \(\alpha\beta=-27\). Thus (\alpha\beta+3\alpha+3\beta=-27+3(6)=-9).
Step 2
Why this answer is correct
The correct answer is A. (-9). Here \(\alpha+\beta=6\) and \(\alpha\beta=-27\). Thus (\alpha\beta+3\alpha+3\beta=-27+3(6)=-9).
Step 3
Exam Tip
यहाँ \(\alpha+\beta=6\) और \(\alpha\beta=-27\) है। इसलिए (\alpha\beta+3\alpha+3\beta=-27+3(6)=-9)।
Login to save your score, XP, coins and progress.
Question 8/18
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि \(x^2-12x+35=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha-5\)\(\beta-5\)) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-12x+35=0\), what is (\(\alpha-5\)\(\beta-5\))?
Explanation opens after your attempt
Step 1
Concept
(\(\alpha-5\)\(\beta-5\)=\alpha\beta-5\(\alpha+\beta\)+25). Here (35-60+25=0).
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\alpha-5\)\(\beta-5\)=\alpha\beta-5\(\alpha+\beta\)+25). Here (35-60+25=0).
Step 3
Exam Tip
(\(\alpha-5\)\(\beta-5\)=\alpha\beta-5\(\alpha+\beta\)+25) है। यहाँ (35-60+25=0)।
Login to save your score, XP, coins and progress.
Question 9/18
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
यदि \(x^2-9x+18=0\) के मूल \(\alpha\) और \(\beta\) हैं, तो (\(\alpha-3\)\(\beta-3\)) का मान क्या है?
If \(\alpha\) and \(\beta\) are roots of \(x^2-9x+18=0\), what is (\(\alpha-3\)\(\beta-3\))?
Explanation opens after your attempt
Step 1
Concept
(\(\alpha-3\)\(\beta-3\)=\alpha\beta-3\(\alpha+\beta\)+9). Here (18-27+9=0).
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\alpha-3\)\(\beta-3\)=\alpha\beta-3\(\alpha+\beta\)+9). Here (18-27+9=0).
Step 3
Exam Tip
(\(\alpha-3\)\(\beta-3\)=\alpha\beta-3\(\alpha+\beta\)+9) है। यहाँ (18-27+9=0)।
Login to save your score, XP, coins and progress.
Question 10/18
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2-4x-21=0\) के मूल \(\alpha,\beta\) हैं, तो \(\alpha\beta+2\alpha+2\beta\) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-4x-21=0\), what is \(\alpha\beta+2\alpha+2\beta\)?
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=4\) and \(\alpha\beta=-21\). Thus (\alpha\beta+2\alpha+2\beta=-21+2(4)=-13).
Step 2
Why this answer is correct
The correct answer is A. (-13). Here \(\alpha+\beta=4\) and \(\alpha\beta=-21\). Thus (\alpha\beta+2\alpha+2\beta=-21+2(4)=-13).
Step 3
Exam Tip
यहाँ \(\alpha+\beta=4\) और \(\alpha\beta=-21\) है। इसलिए (\alpha\beta+2\alpha+2\beta=-21+2(4)=-13)।
Login to save your score, XP, coins and progress.
Question 11/18
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2-9x+20=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha-4\)\(\beta-4\)) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-9x+20=0\), what is (\(\alpha-4\)\(\beta-4\))?
Explanation opens after your attempt
Step 1
Concept
(\(\alpha-4\)\(\beta-4\)=\alpha\beta-4\(\alpha+\beta\)+16). Here (20-36+16=0).
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\alpha-4\)\(\beta-4\)=\alpha\beta-4\(\alpha+\beta\)+16). Here (20-36+16=0).
Step 3
Exam Tip
(\(\alpha-4\)\(\beta-4\)=\alpha\beta-4\(\alpha+\beta\)+16) है। यहाँ (20-36+16=0)।
Login to save your score, XP, coins and progress.
Question 12/18
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि \(x^2+7x+10=0\) के मूल \(\alpha\) और \(\beta\) हैं, तो (\(\alpha+2\)\(\beta+2\)) का मान क्या है?
If \(\alpha\) and \(\beta\) are roots of \(x^2+7x+10=0\), what is (\(\alpha+2\)\(\beta+2\))?
Explanation opens after your attempt
Step 1
Concept
(\(\alpha+2\)\(\beta+2\)=\alpha\beta+2\(\alpha+\beta\)+4). Here (10+2(-7)+4=0).
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\alpha+2\)\(\beta+2\)=\alpha\beta+2\(\alpha+\beta\)+4). Here (10+2(-7)+4=0).
Step 3
Exam Tip
(\(\alpha+2\)\(\beta+2\)=\alpha\beta+2\(\alpha+\beta\)+4) होता है। यहाँ (10+2(-7)+4=0)।
Login to save your score, XP, coins and progress.
Question 13/18
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2+3x-18=0\) के मूल \(\alpha,\beta\) हैं, तो \(\alpha\beta-\alpha-\beta\) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2+3x-18=0\), what is \(\alpha\beta-\alpha-\beta\)?
Explanation opens after your attempt
Step 1
Concept
Here \(\alpha+\beta=-3\) and \(\alpha\beta=-18\). Thus (\alpha\beta-\alpha-\beta=-18-(-3)=-15).
Step 2
Why this answer is correct
The correct answer is A. (-15). Here \(\alpha+\beta=-3\) and \(\alpha\beta=-18\). Thus (\alpha\beta-\alpha-\beta=-18-(-3)=-15).
Step 3
Exam Tip
यहाँ \(\alpha+\beta=-3\) और \(\alpha\beta=-18\) है। इसलिए (\alpha\beta-\alpha-\beta=-18-(-3)=-15)।
Login to save your score, XP, coins and progress.
Question 14/18
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2-10x+21=0\) के मूल \(\alpha,\beta\) हैं, तो (\(\alpha-3\)\(\beta-3\)) का मान क्या है?
If \(\alpha,\beta\) are roots of \(x^2-10x+21=0\), what is (\(\alpha-3\)\(\beta-3\))?
Explanation opens after your attempt
Step 1
Concept
(\(\alpha-3\)\(\beta-3\)=\alpha\beta-3\(\alpha+\beta\)+9). Here (21-30+9=0).
Step 2
Why this answer is correct
The correct answer is A. (0). (\(\alpha-3\)\(\beta-3\)=\alpha\beta-3\(\alpha+\beta\)+9). Here (21-30+9=0).
Step 3
Exam Tip
(\(\alpha-3\)\(\beta-3\)=\alpha\beta-3\(\alpha+\beta\)+9) है। यहाँ (21-30+9=0)।
Login to save your score, XP, coins and progress.
Question 15/18
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि \(x^2-8x+15=0\) के मूल \(\alpha\) और \(\beta\) हैं, तो (\(\alpha-1\)\(\beta-1\)) का मान क्या है?
If \(\alpha\) and \(\beta\) are roots of \(x^2-8x+15=0\), what is (\(\alpha-1\)\(\beta-1\))?
Explanation opens after your attempt
Step 1
Concept
(\(\alpha-1\)\(\beta-1\)=\alpha\beta-\(\alpha+\beta\)+1). Here (15-8+1=8).
Step 2
Why this answer is correct
The correct answer is A. (8). (\(\alpha-1\)\(\beta-1\)=\alpha\beta-\(\alpha+\beta\)+1). Here (15-8+1=8).
Step 3
Exam Tip
(\(\alpha-1\)\(\beta-1\)=\alpha\beta-\(\alpha+\beta\)+1) होता है। यहाँ (15-8+1=8)।
Login to save your score, XP, coins and progress.
Question 16/18
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
समीकरण \(7x^2-5x+2=0\) में \(b^2+ac\) का मान क्या है?
What is the value of \(b^2+ac\) in \(7x^2-5x+2=0\)?
Explanation opens after your attempt
Step 1
Concept
Here (a=7), (b=-5), (c=2), so \(b^2+ac=25+14=39\). In \(b^2\), the negative sign becomes positive after squaring.
Step 2
Why this answer is correct
The correct answer is A. (39). Here (a=7), (b=-5), (c=2), so \(b^2+ac=25+14=39\). In \(b^2\), the negative sign becomes positive after squaring.
Step 3
Exam Tip
यहाँ (a=7), (b=-5), (c=2) हैं, इसलिए \(b^2+ac=25+14=39\) है। \(b^2\) में ऋण चिन्ह वर्ग के कारण धनात्मक हो जाता है।
Login to save your score, XP, coins and progress.
Question 17/18
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
समीकरण \(4x^2-2x-6=0\) में (a-b+c) का मान क्या है?
What is the value of (a-b+c) for \(4x^2-2x-6=0\)?
Explanation opens after your attempt
Step 1
Concept
Here (a=4), (b=-2), (c=-6). Thus (a-b+c=4-(-2)-6=0).
Step 2
Why this answer is correct
The correct answer is A. (0). Here (a=4), (b=-2), (c=-6). Thus (a-b+c=4-(-2)-6=0).
Step 3
Exam Tip
यहां (a=4), (b=-2), (c=-6) हैं। इसलिए (a-b+c=4-(-2)-6=0) है।
Login to save your score, XP, coins and progress.
Question 18/18
Easy Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
समीकरण \(2x^2-3x-5=0\) में (a-b+c) का मान क्या है?
What is the value of (a-b+c) for \(2x^2-3x-5=0\)?
Explanation opens after your attempt
Step 1
Concept
Here (a=2), (b=-3), (c=-5). Thus (a-b+c=2-(-3)-5=0).
Step 2
Why this answer is correct
The correct answer is A. (0). Here (a=2), (b=-3), (c=-5). Thus (a-b+c=2-(-3)-5=0).
Step 3
Exam Tip
यहां (a=2), (b=-3), (c=-5) हैं। इसलिए (a-b+c=2-(-3)-5=0) है।
Login to save your score, XP, coins and progress.
