TestUstad

The sum of the squares of two consecutive positive integers exceeds their product by 91. Find the integers?

Correct answer: A. 9, 10

  • A. 9, 10
  • B. 10, 11
  • C. 11, 12
  • D. 12, 13

Explanation

Let the consecutive positive integers be n and n + 1. Their square sum exceeds their product by n² + (n + 1)² - n(n + 1) = n² + n + 1 = 91, so n² + n - 90 = 0 and (n + 10)(n - 9) = 0; positivity gives n = 9, hence 9 and 10. The likely mistake is choosing b by adding the two integers or comparing the square sum without subtracting the product.

Written and checked by , MS Computer ScienceLast updated
Report an error

The more specific you are, the faster it gets fixed. A source beats an opinion.

Prefer email? [email protected]

About Quadratic Equations

Quadratic equations contain a squared variable and can be solved by factorisation, completing the square, the quadratic formula, or graphical reasoning. Questions cover roots, the discriminant, and the relationship between roots and coefficients, while distinguishing real and repeated roots from complex or non-real roots.

Practise Algebra

269 free Algebra MCQs from Mathematics, each with the correct answer and an explanation. Unlimited attempts, no account needed.

Start a free Algebra testAll Algebra MCQs

Discussion

Stuck on an option, or know a faster way to get there? Ask or explain it here.

No comments yet. Be the first to explain this one.

Exams that ask Mathematics questions like this

Mathematics is on 76 papers prepared for on TestUstad, and all of them draw the same bank, so this question is worth knowing for every one of them.

Lecturer Mathematics Test Mathematics80 MCQsNET Mathematics80 MCQsSubject Specialist Mathematics Test Mathematics80 MCQsATS Mathematics30 MCQsCA QAT Mathematics30 MCQsCTS Mathematics30 MCQsECAT Mathematics30 MCQsETEA Engineering Admission Test Mathematics30 MCQsETEA Recruitment Tests Mathematics30 MCQsGAT General Mathematics30 MCQsGIKI Mathematics30 MCQsNAT Mathematics30 MCQsNED Mathematics30 MCQsNTS Mathematics30 MCQsOTS Mathematics30 MCQsPIEAS Mathematics30 MCQsPTS Mathematics30 MCQsSTS Mathematics30 MCQsUTS Mathematics30 MCQsBCAT Mathematics25 MCQsISSB Mathematics25 MCQsCSS MPT Mathematics20 MCQsPAF Mathematics20 MCQsPAF Airman Mathematics20 MCQsPakistan Army Commissioned Officer Test Mathematics20 MCQsPakistan Navy Test Mathematics20 MCQsPatwari Test Mathematics20 MCQsPMA Long Course Test Mathematics20 MCQsPMD Mathematics20 MCQsComputer Operator Test Mathematics15 MCQsDEO Mathematics15 MCQsEducators ESE Test Mathematics15 MCQsEducators SESE Test Mathematics15 MCQsEducators SST Test Mathematics15 MCQsFBR Mathematics15 MCQsJEST Mathematics15 MCQsJunior Clerk Test Mathematics15 MCQsLAT Mathematics15 MCQsNADRA Mathematics15 MCQsPST Mathematics15 MCQsSub Registrar Test Mathematics15 MCQsAJKPSC Mathematics10 MCQsAssistant BS-16 Test Mathematics10 MCQsBPSC Mathematics10 MCQsECP Mathematics10 MCQsFIA Mathematics10 MCQsFPSC Mathematics10 MCQsGBPSC Mathematics10 MCQsIB Mathematics10 MCQsIntelligence Officer Mathematics10 MCQsKPPSC Mathematics10 MCQsMES Mathematics10 MCQsNAB Mathematics10 MCQsNational Highways and Motorway Police Test Mathematics10 MCQsPakistan Railways Recruitment Test Mathematics10 MCQsPCS Mathematics10 MCQsPIA Mathematics10 MCQsPPSC Mathematics10 MCQsPunjab Police ASI Test Mathematics10 MCQsPunjab Police Sub Inspector Test Mathematics10 MCQsSNGPL Mathematics10 MCQsSPSC Mathematics10 MCQsSub Engineer Civil Test Mathematics10 MCQsSub Engineer Electrical Test Mathematics10 MCQsSub Engineer Mechanical Test Mathematics10 MCQsTehsildar and Naib Tehsildar Test Mathematics10 MCQsWAPDA Mathematics10 MCQsANF Mathematics5 MCQsASF Mathematics5 MCQsCTD Mathematics5 MCQsElite Police Force Test Mathematics5 MCQsPakistan Army Soldier Test Mathematics5 MCQsPakistan Rangers Test Mathematics5 MCQsPERA Force Test Mathematics5 MCQsPunjab Police Constable Test Mathematics5 MCQsRescue 1122 Test Mathematics5 MCQs

More Quadratic Equations questions

One root of the quadratic equation x2 - 12x + a = 0, is thrice the other. Find the value of a?

If a and b are the roots of the equation x2 - 9x + 20 = 0, find the value of a2 + b2 + ab?

Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 8x + 4 = 0?

If the roots of the equation 2x2 - 5x + b = 0 are in the ratio of 2:3, then find the value of b?

The sum and the product of the roots of the quadratic equation x(power 2) + 20x + 3 = 0 are?

If the roots of a quadratic equation are 20 and -7, then find the equation?