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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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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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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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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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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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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\(\frac{1}{2}\) 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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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