Question 1/39
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि \(x^2+px+q=0\) की जड़ें (-4) और (9) हैं, तो (p-q) का मान क्या है?
If the roots of \(x^2+px+q=0\) are (-4) and (9), what is the value of (p-q)?
#quadratic-roots
#coefficients
#forming-equation
A (31)
B (33)
C (35)
D (41)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (5), so (p=-5). The product is (-36), so (q=-36), hence (p-q=31).
Step 2
Why this answer is correct
The correct answer is A. (31). The sum of roots is (5), so (p=-5). The product is (-36), so (q=-36), hence (p-q=31).
Step 3
Exam Tip
जड़ों का योग (5) है, इसलिए (p=-5)। गुणनफल (-36) है, इसलिए (q=-36), अतः (p-q=31)।
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Question 2/39
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि किसी द्विघात समीकरण की जड़ें एक-दूसरे की व्युत्क्रम हैं और उनका योग \(\frac{5}{2}\) है, तो समीकरण कौन-सा हो सकता है?
If the roots of a quadratic equation are reciprocals of each other and their sum is \(\frac{5}{2}\), which equation is possible?
#quadratic-roots
#reciprocal-roots
#forming-equation
A \(2x^2-5x+2=0\)
B \(2x^2+5x+2=0\)
C \(x^2-5x+2=0\)
D \(5x^2-2x+2=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-5x+2=0\)
Step 1
Concept
Reciprocal roots have product (1). Multiplying \(x^2-\frac{5}{2}x+1=0\) by (2) gives \(2x^2-5x+2=0\).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-5x+2=0\). Reciprocal roots have product (1). Multiplying \(x^2-\frac{5}{2}x+1=0\) by (2) gives \(2x^2-5x+2=0\).
Step 3
Exam Tip
व्युत्क्रम जड़ों का गुणनफल (1) होता है। समीकरण \(x^2-\frac{5}{2}x+1=0\) को (2) से गुणा करने पर \(2x^2-5x+2=0\) मिलता है।
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Question 3/39
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि किसी द्विघात समीकरण की जड़ों का योग (7) और गुणनफल (10) है, तो समीकरण कौन-सा है?
If the sum of roots of a quadratic equation is (7) and the product is (10), which is the equation?
#quadratic-roots
#forming-equation
#sum-product
A \(x^2+7x+10=0\)
B \(x^2-10x+7=0\)
C \(x^2-7x+10=0\)
D \(x^2+10x-7=0\)
Explanation opens after your attempt
Correct Answer
C. \(x^2-7x+10=0\)
Step 1
Concept
\(The equation is (x^2-(\)sum)x+product\(=0). Hence (x^2-7x+10=0) is correct.\)
Step 2
Why this answer is correct
\(The correct answer is C. (x^2-7x+10=0). The equation is (x^2-(\)sum)x+product\(=0). Hence (x^2-7x+10=0) is correct.\)
Step 3
Exam Tip
\(जड़ों का समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(इसलिए (x^2-7x+10=0) सही है\)।
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Question 4/39
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 32
यदि \(x^2+px+q=0\) की जड़ें (-3) और (7) हैं, तो (p-q) का मान क्या है?
If the roots of \(x^2+px+q=0\) are (-3) and (7), what is the value of (p-q)?
#quadratic-roots
#coefficients
#forming-equation
A (13)
B (15)
C (17)
D (21)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (4), so (p=-4). The product is (-21), so (q=-21), hence (p-q=17).
Step 2
Why this answer is correct
The correct answer is C. (17). The sum of roots is (4), so (p=-4). The product is (-21), so (q=-21), hence (p-q=17).
Step 3
Exam Tip
जड़ों का योग (4) है, इसलिए (p=-4)। गुणनफल (-21) है, इसलिए (q=-21), अतः (p-q=17)।
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Question 5/39
Expert Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 31
यदि \(x^2+px+q=0\) की जड़ें (-2) और (5) हैं, तो (p-q) का मान क्या है?
If the roots of \(x^2+px+q=0\) are (-2) and (5), what is (p-q)?
#quadratic-roots
#coefficients
#forming-equation
A (7)
B (-7)
C (13)
D (-13)
Explanation opens after your attempt
Step 1
Concept
The sum of roots is (3), so (p=-3). The product is (-10), so (q=-10), hence (p-q=7).
Step 2
Why this answer is correct
The correct answer is A. (7). The sum of roots is (3), so (p=-3). The product is (-10), so (q=-10), hence (p-q=7).
Step 3
Exam Tip
जड़ों का योग (3) है, इसलिए (p=-3)। गुणनफल (-10) है, इसलिए (q=-10), अतः (p-q=7)।
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Question 6/39
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि किसी द्विघात समीकरण की जड़ें (3) और (-2) हैं और \(x^2\) का गुणांक (2) है, तो समीकरण कौन-सा है?
If the roots of a quadratic equation are (3) and (-2), and the coefficient of \(x^2\) is (2), which is the equation?
#quadratic-roots
#forming-equation
#leading-coefficient
A \(2x^2-2x-12=0\)
B \(2x^2+2x-12=0\)
C \(2x^2-2x+12=0\)
D \(x^2-x-6=0\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-2x-12=0\)
Step 1
Concept
The monic equation is \(x^2-x-6=0\). Since the coefficient of \(x^2\) must be (2), multiply the whole equation by (2).
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-2x-12=0\). The monic equation is \(x^2-x-6=0\). Since the coefficient of \(x^2\) must be (2), multiply the whole equation by (2).
Step 3
Exam Tip
मॉनिक समीकरण \(x^2-x-6=0\) है। \(x^2\) का गुणांक (2) चाहिए, इसलिए पूरे समीकरण को (2) से गुणा करें।
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Question 7/39
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
\(\frac{1}{2}\) और \(\frac{3}{4}\) जड़ों वाला द्विघात समीकरण कौन-सा है?
Which quadratic equation has roots \(\frac{1}{2}\) and \(\frac{3}{4}\)?
#quadratic-roots
#forming-equation
#fractional-roots
A \(8x^2-10x+3=0\)
B \(8x^2+10x+3=0\)
C \(4x^2-10x+3=0\)
D \(8x^2-6x+3=0\)
Explanation opens after your attempt
Correct Answer
A. \(8x^2-10x+3=0\)
Step 1
Concept
The sum is \(\frac{5}{4}\) and the product is \(\frac{3}{8}\). Multiply \(x^2-\frac{5}{4}x+\frac{3}{8}=0\) by (8).
Step 2
Why this answer is correct
The correct answer is A. \(8x^2-10x+3=0\). The sum is \(\frac{5}{4}\) and the product is \(\frac{3}{8}\). Multiply \(x^2-\frac{5}{4}x+\frac{3}{8}=0\) by (8).
Step 3
Exam Tip
जड़ों का योग \(\frac{5}{4}\) और गुणनफल \(\frac{3}{8}\) है। समीकरण \(x^2-\frac{5}{4}x+\frac{3}{8}=0\) को (8) से गुणा करें।
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Question 8/39
Hard Mathematics
Quadratic Equations Roots of a Quadratic Equation Class 10 Level 33
यदि किसी द्विघात समीकरण की जड़ें \(2+\sqrt{5}\) और \(2-\sqrt{5}\) हैं, तो समीकरण कौन-सा है?
If the roots of a quadratic equation are \(2+\sqrt{5}\) and \(2-\sqrt{5}\), which is the equation?
#quadratic-roots
#forming-equation
#surd-roots
A \(x^2-4x-1=0\)
B \(x^2+4x-1=0\)
C \(x^2-4x+1=0\)
D \(x^2+4x+1=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-4x-1=0\)
Step 1
Concept
\(The sum of roots is (4) and the product is (-1). Use (x^2-(\)sum)x+product\(=0) to get the answer.\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-4x-1=0). The sum of roots is (4) and the product is (-1). Use (x^2-(\)sum)x+product\(=0) to get the answer.\)
Step 3
Exam Tip
जड़ों का योग (4) और गुणनफल (-1) है। \(समीकरण (x^2-(\)योग)x+गुणनफल\(=0) से उत्तर मिलता है\)।
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Question 9/39
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
किस द्विघात समीकरण के मूलों का योग (0) और गुणनफल (-169) है?
Which quadratic equation has sum of roots (0) and product (-169)?
#quadratic-equations
#sum-product
#forming-equation
#expert
A \(x^2-169=0\)
B \(x^2+169=0\)
C \(x^2+13x-169=0\)
D \(x^2-13x-169=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-169=0\)
Step 1
Concept
\(The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-169) gives (x^2-169=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-169=0). The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-169) gives (x^2-169=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) है। \(योग (0) और गुणनफल (-169) रखने पर (x^2-169=0) मिलता है\)।
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Question 10/39
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
दो संख्याओं का योग (19) और गुणनफल (90) है। वे किस द्विघात समीकरण के मूल हो सकते हैं?
Two numbers have sum (19) and product (90). They can be roots of which quadratic equation?
#quadratic-equations
#forming-equation
#sum-product
#expert
A \(x^2-19x+90=0\)
B \(x^2+19x+90=0\)
C \(x^2-90x+19=0\)
D \(x^2+90x-19=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-19x+90=0\)
Step 1
Concept
If the sum of roots is (19) and product is (90), the equation is \(x^2-19x+90=0\). Remember the monic form formula.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-19x+90=0\). If the sum of roots is (19) and product is (90), the equation is \(x^2-19x+90=0\). Remember the monic form formula.
Step 3
Exam Tip
यदि मूलों का योग (19) और गुणनफल (90) है, तो समीकरण \(x^2-19x+90=0\) होगा। मोनिक रूप का सूत्र याद रखें।
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Question 11/39
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
मूलों का योग (-15) और गुणनफल (56) वाला मोनिक द्विघात समीकरण कौन-सा है?
Which monic quadratic equation has sum of roots (-15) and product (56)?
#quadratic-equations
#sum-product
#forming-equation
#expert
A \(x^2+15x+56=0\)
B \(x^2-15x+56=0\)
C \(x^2+56x+15=0\)
D \(x^2-56x+15=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+15x+56=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-15) gives (x^2+15x+56=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2+15x+56=0). A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-15) gives (x^2+15x+56=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(योग (-15) रखने पर (x^2+15x+56=0) मिलता है\)।
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Question 12/39
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
किस द्विघात समीकरण के मूलों का योग (0) और गुणनफल (-144) है?
Which quadratic equation has sum of roots (0) and product (-144)?
#quadratic-equations
#sum-product
#forming-equation
#expert
A \(x^2-144=0\)
B \(x^2+144=0\)
C \(x^2+12x-144=0\)
D \(x^2-12x-144=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-144=0\)
Step 1
Concept
\(The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-144) gives (x^2-144=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-144=0). The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-144) gives (x^2-144=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) है। \(योग (0) और गुणनफल (-144) रखने पर (x^2-144=0) मिलता है\)।
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Question 13/39
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
दो संख्याओं का योग (17) और गुणनफल (72) है। वे किस द्विघात समीकरण के मूल हो सकते हैं?
Two numbers have sum (17) and product (72). They can be roots of which quadratic equation?
#quadratic-equations
#forming-equation
#sum-product
#expert
A \(x^2-17x+72=0\)
B \(x^2+17x+72=0\)
C \(x^2-72x+17=0\)
D \(x^2+72x-17=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-17x+72=0\)
Step 1
Concept
If the sum of roots is (17) and product is (72), the equation is \(x^2-17x+72=0\). Remember the monic form formula.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-17x+72=0\). If the sum of roots is (17) and product is (72), the equation is \(x^2-17x+72=0\). Remember the monic form formula.
Step 3
Exam Tip
यदि मूलों का योग (17) और गुणनफल (72) है, तो समीकरण \(x^2-17x+72=0\) होगा। मोनिक रूप का सूत्र याद रखें।
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Question 14/39
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
मूलों का योग (-13) और गुणनफल (42) वाला मोनिक द्विघात समीकरण कौन-सा है?
Which monic quadratic equation has sum of roots (-13) and product (42)?
#quadratic-equations
#sum-product
#forming-equation
#expert
A \(x^2+13x+42=0\)
B \(x^2-13x+42=0\)
C \(x^2+42x+13=0\)
D \(x^2-42x+13=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+13x+42=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-13) gives (x^2+13x+42=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2+13x+42=0). A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-13) gives (x^2+13x+42=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(योग (-13) रखने पर (x^2+13x+42=0) मिलता है\)।
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Question 15/39
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
किस द्विघात समीकरण के मूलों का योग (0) और गुणनफल (-121) है?
Which quadratic equation has sum of roots (0) and product (-121)?
#quadratic-equations
#sum-product
#forming-equation
#expert
A \(x^2-121=0\)
B \(x^2+121=0\)
C \(x^2+11x-121=0\)
D \(x^2-11x-121=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-121=0\)
Step 1
Concept
\(The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-121) gives (x^2-121=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-121=0). The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-121) gives (x^2-121=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) है। \(योग (0) और गुणनफल (-121) रखने पर (x^2-121=0) मिलता है\)।
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Question 16/39
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
दो संख्याओं का योग (15) और गुणनफल (54) है। वे किस द्विघात समीकरण के मूल हो सकते हैं?
Two numbers have sum (15) and product (54). They can be roots of which quadratic equation?
#quadratic-equations
#forming-equation
#sum-product
#expert
A \(x^2-15x+54=0\)
B \(x^2+15x+54=0\)
C \(x^2-54x+15=0\)
D \(x^2+54x-15=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-15x+54=0\)
Step 1
Concept
If the sum of roots is (15) and product is (54), the equation is \(x^2-15x+54=0\). Remember the monic form formula.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-15x+54=0\). If the sum of roots is (15) and product is (54), the equation is \(x^2-15x+54=0\). Remember the monic form formula.
Step 3
Exam Tip
यदि मूलों का योग (15) और गुणनफल (54) है, तो समीकरण \(x^2-15x+54=0\) होगा। मोनिक रूप का सूत्र याद रखें।
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Question 17/39
Expert Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
मूलों का योग (-11) और गुणनफल (30) वाला मोनिक द्विघात समीकरण कौन-सा है?
Which monic quadratic equation has sum of roots (-11) and product (30)?
#quadratic-equations
#sum-product
#forming-equation
#expert
A \(x^2+11x+30=0\)
B \(x^2-11x+30=0\)
C \(x^2+30x+11=0\)
D \(x^2-30x+11=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+11x+30=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-11) gives (x^2+11x+30=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2+11x+30=0). A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-11) gives (x^2+11x+30=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(योग (-11) रखने पर (x^2+11x+30=0) मिलता है\)।
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Question 18/39
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
किस द्विघात समीकरण के मूलों का योग (0) और गुणनफल (-81) है?
Which quadratic equation has sum of roots (0) and product (-81)?
#quadratic-equations
#sum-product
#forming-equation
#hard
A \(x^2-81=0\)
B \(x^2+81=0\)
C \(x^2+9x-81=0\)
D \(x^2-9x-81=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-81=0\)
Step 1
Concept
\(The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-81) gives (x^2-81=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-81=0). The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-81) gives (x^2-81=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) है। \(योग (0) और गुणनफल (-81) रखने पर (x^2-81=0) मिलता है\)।
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Question 19/39
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
दो संख्याओं का योग (13) और गुणनफल (40) है। वे किस द्विघात समीकरण के मूल हो सकते हैं?
Two numbers have sum (13) and product (40). They can be roots of which quadratic equation?
#quadratic-equations
#forming-equation
#sum-product
#hard
A \(x^2-13x+40=0\)
B \(x^2+13x+40=0\)
C \(x^2-40x+13=0\)
D \(x^2+40x-13=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-13x+40=0\)
Step 1
Concept
If the sum of roots is (13) and product is (40), the equation is \(x^2-13x+40=0\). Remember the monic form formula.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-13x+40=0\). If the sum of roots is (13) and product is (40), the equation is \(x^2-13x+40=0\). Remember the monic form formula.
Step 3
Exam Tip
यदि मूलों का योग (13) और गुणनफल (40) है, तो समीकरण \(x^2-13x+40=0\) होगा। मोनिक रूप का सूत्र याद रखें।
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Question 20/39
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
मूलों का योग (-9) और गुणनफल (20) वाला मोनिक द्विघात समीकरण कौन-सा है?
Which monic quadratic equation has sum of roots (-9) and product (20)?
#quadratic-equations
#sum-product
#forming-equation
#hard
A \(x^2+9x+20=0\)
B \(x^2-9x+20=0\)
C \(x^2+20x+9=0\)
D \(x^2-20x+9=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+9x+20=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-9) gives (x^2+9x+20=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2+9x+20=0). A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-9) gives (x^2+9x+20=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(योग (-9) रखने पर (x^2+9x+20=0) मिलता है\)।
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Question 21/39
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
किस द्विघात समीकरण के मूलों का योग (0) और गुणनफल (-49) है?
Which quadratic equation has sum of roots (0) and product (-49)?
#quadratic-equations
#sum-product
#forming-equation
#hard
A \(x^2-49=0\)
B \(x^2+49=0\)
C \(x^2+7x-49=0\)
D \(x^2-7x-49=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-49=0\)
Step 1
Concept
\(The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-49) gives (x^2-49=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-49=0). The monic equation is (x^2-(\)sum)x+product\(=0). Using sum (0) and product (-49) gives (x^2-49=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) है। \(योग (0) और गुणनफल (-49) रखने पर (x^2-49=0) मिलता है\)।
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Question 22/39
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
दो संख्याओं का योग (11) और गुणनफल (30) है। वे किस द्विघात समीकरण के मूल हो सकते हैं?
Two numbers have sum (11) and product (30). They can be roots of which quadratic equation?
#quadratic-equations
#forming-equation
#sum-product
#hard
A \(x^2-11x+30=0\)
B \(x^2+11x+30=0\)
C \(x^2-30x+11=0\)
D \(x^2+30x-11=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-11x+30=0\)
Step 1
Concept
If the sum of roots is (11) and product is (30), the equation is \(x^2-11x+30=0\). Remember the monic form formula.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-11x+30=0\). If the sum of roots is (11) and product is (30), the equation is \(x^2-11x+30=0\). Remember the monic form formula.
Step 3
Exam Tip
यदि मूलों का योग (11) और गुणनफल (30) है, तो समीकरण \(x^2-11x+30=0\) होगा। मोनिक रूप का सूत्र याद रखें।
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Question 23/39
Hard Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
मूलों का योग (7) और गुणनफल (10) वाला मोनिक द्विघात समीकरण कौन-सा है?
Which monic quadratic equation has sum of roots (7) and product (10)?
#quadratic-equations
#sum-product
#forming-equation
#hard
A \(x^2-7x+10=0\)
B \(x^2+7x+10=0\)
C \(x^2-10x+7=0\)
D \(x^2+10x-7=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-7x+10=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2-7x+10=0) is correct.\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-7x+10=0). A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2-7x+10=0) is correct.\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(इसलिए (x^2-7x+10=0) सही है\)।
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Question 24/39
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
किस द्विघात समीकरण में मूलों का योग (-8) और गुणनफल (15) है?
Which quadratic equation has sum of roots (-8) and product (15)?
#quadratic-equations
#sum-product
#forming-equation
#medium
A \(x^2+8x+15=0\)
B \(x^2-8x+15=0\)
C \(x^2+15x+8=0\)
D \(x^2-15x+8=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+8x+15=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-8) gives (x^2+8x+15=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2+8x+15=0). A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-8) gives (x^2+8x+15=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(योग (-8) रखने पर (x^2+8x+15=0) मिलता है\)।
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Question 25/39
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
किस विकल्प में (x=3) और (x=8) मूल हैं?
Which option has roots (x=3) and (x=8)?
#quadratic-equations
#roots
#forming-equation
#medium
A \(x^2-11x+24=0\)
B \(x^2+11x+24=0\)
C \(x^2-24x+11=0\)
D \(x^2+24x-11=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-11x+24=0\)
Step 1
Concept
If the roots are (3) and (8), the factors are ((x-3)) and ((x-8)). Their product gives \(x^2-11x+24=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-11x+24=0\). If the roots are (3) and (8), the factors are ((x-3)) and ((x-8)). Their product gives \(x^2-11x+24=0\).
Step 3
Exam Tip
मूल (3) और (8) हों तो गुणनखंड ((x-3)) और ((x-8)) होंगे। इनका गुणन \(x^2-11x+24=0\) देता है।
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Question 26/39
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 30
यदि (a=-2), (b=9), (c=-7) हैं, तो संबंधित द्विघात समीकरण कौन-सा है?
If (a=-2), (b=9), (c=-7), which is the corresponding quadratic equation?
#quadratic-equations
#forming-equation
#coefficients
#medium
A \(2x^2+9x-7=0\)
B \(-2x^2+9x-7=0\)
C \(-2x^2-9x-7=0\)
D \(7x^2+9x-2=0\)
Explanation opens after your attempt
Correct Answer
B. \(-2x^2+9x-7=0\)
Step 1
Concept
Substituting in \(ax^2+bx+c=0\) gives \(-2x^2+9x-7=0\). Never ignore the sign of a coefficient.
Step 2
Why this answer is correct
The correct answer is B. \(-2x^2+9x-7=0\). Substituting in \(ax^2+bx+c=0\) gives \(-2x^2+9x-7=0\). Never ignore the sign of a coefficient.
Step 3
Exam Tip
मानक रूप \(ax^2+bx+c=0\) में मान रखने पर \(-2x^2+9x-7=0\) मिलता है। गुणांक का चिन्ह कभी न छोड़ें।
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Question 27/39
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
किस द्विघात समीकरण में मूलों का योग (-6) और गुणनफल (8) है?
Which quadratic equation has sum of roots (-6) and product (8)?
#quadratic-equations
#sum-product
#forming-equation
#medium
A \(x^2+6x+8=0\)
B \(x^2-6x+8=0\)
C \(x^2+8x+6=0\)
D \(x^2-8x+6=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+6x+8=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-6) gives (x^2+6x+8=0).\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2+6x+8=0). A monic equation is (x^2-(\)sum)x+product\(=0). Substituting sum (-6) gives (x^2+6x+8=0).\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(योग (-6) रखने पर (x^2+6x+8=0) मिलता है\)।
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Question 28/39
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
किस विकल्प में (x=2) और (x=7) मूल हैं?
Which option has roots (x=2) and (x=7)?
#quadratic-equations
#roots
#forming-equation
#medium
A \(x^2-9x+14=0\)
B \(x^2+9x+14=0\)
C \(x^2-14x+9=0\)
D \(x^2+14x-9=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-9x+14=0\)
Step 1
Concept
If the roots are (2) and (7), the factors are ((x-2)) and ((x-7)). Their product gives \(x^2-9x+14=0\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-9x+14=0\). If the roots are (2) and (7), the factors are ((x-2)) and ((x-7)). Their product gives \(x^2-9x+14=0\).
Step 3
Exam Tip
मूल (2) और (7) हों तो गुणनखंड ((x-2)) और ((x-7)) होंगे। इनका गुणन \(x^2-9x+14=0\) देता है।
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Question 29/39
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 29
यदि (a=5), (b=-11), (c=-6) हैं, तो संबंधित द्विघात समीकरण कौन-सा है?
If (a=5), (b=-11), (c=-6), which is the corresponding quadratic equation?
#quadratic-equations
#forming-equation
#coefficients
#medium
A \(5x^2+11x-6=0\)
B \(5x^2-11x-6=0\)
C \(6x^2-11x-5=0\)
D \(5x^2-6x-11=0\)
Explanation opens after your attempt
Correct Answer
B. \(5x^2-11x-6=0\)
Step 1
Concept
Substituting into \(ax^2+bx+c=0\) gives \(5x^2-11x-6=0\). Treat the negative sign as part of the coefficient.
Step 2
Why this answer is correct
The correct answer is B. \(5x^2-11x-6=0\). Substituting into \(ax^2+bx+c=0\) gives \(5x^2-11x-6=0\). Treat the negative sign as part of the coefficient.
Step 3
Exam Tip
मानक रूप \(ax^2+bx+c=0\) में मान रखने पर \(5x^2-11x-6=0\) मिलता है। ऋण चिन्ह को गुणांक का भाग मानें।
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Question 30/39
Medium Mathematics
Quadratic Equations Introduction to Quadratic Equations Class 10 Level 28
किस द्विघात समीकरण में मूलों का योग (5) और गुणनफल (6) है?
Which quadratic equation has sum of roots (5) and product (6)?
#quadratic-equations
#sum-product
#forming-equation
#medium
A \(x^2-5x+6=0\)
B \(x^2+5x+6=0\)
C \(x^2-6x+5=0\)
D \(x^2+6x+5=0\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-5x+6=0\)
Step 1
Concept
\(A monic equation is (x^2-(\)sum)x+product\(=0). Hence (x^2-5x+6=0) is correct.\)
Step 2
Why this answer is correct
\(The correct answer is A. (x^2-5x+6=0). A monic equation is (x^2-(\)sum)x+product\(=0). Hence (x^2-5x+6=0) is correct.\)
Step 3
Exam Tip
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। \(इसलिए (x^2-5x+6=0) सही है\)।
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