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CA Foundation Quadratic Equation — practice questions — page 2

Explore 52 free Quadratic Equation questions in CA Foundation Quantitative Aptitude. Open each question or exercise to read its content, reference answers and available explanation.

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Quadratic Equation questions and exercises with answers

Showing questions 31–52 of 52.

Who independently derived the trigonometric solution for a cubic with three real roots?Read the answer and worked solution →Which Persian poet-mathematician found that a cubic can have more than one solution?Read the answer and worked solution →Which Tang dynasty mathematician numerically solved 25 cubic equations?Read the answer and worked solution →Which cubic example did Bhaskara II give?Read the answer and worked solution →Which cubic did Fibonacci approximate in his book Flos?Read the answer and worked solution →Babylonian cuneiform tablets for cubics heldRead the answer and worked solution →Problems solvable by quadratic equations were known as early asRead the answer and worked solution →A depressed cubic has no term inRead the answer and worked solution →A change of variable reducing a cubic to depressed form is aRead the answer and worked solution →To depress x³ + 6x² + 9x + 2 = 0, substitute x =Read the answer and worked solution →The depressing substitution centres a cubic on itsRead the answer and worked solution →If a real quadratic has negative discriminant, its roots areRead the answer and worked solution →With rational coefficients and a perfect square discriminant, the roots areRead the answer and worked solution →To complete the square on x² + 6x = 7, add what to both sides?Read the answer and worked solution →Dividing ax² + bx + c = 0 by a gives x² + px + q = 0, where p and q areRead the answer and worked solution →If α and β are roots of x² − 5x + 4 = 0, then α² + β² isRead the answer and worked solution →A father is 3 times his son's age. In 10 years he will be twice as old. The son is nowRead the answer and worked solution →A rectangle has perimeter 34 m and area 60 m². Its longer side isRead the answer and worked solution →The product of two consecutive positive integers is 132. The smaller isRead the answer and worked solution →A number plus its reciprocal is 5/2. The greater such number isRead the answer and worked solution →How many real roots does x³ − 8 = 0 have?Read the answer and worked solution →The cubic (x − 2)²(x + 5) = 0 has the repeated rootRead the answer and worked solution →

Worked practice questions

Who independently derived the trigonometric solution for a cubic with three real roots?

  1. Tartaglia
  2. Bombelli
  3. François Viète
  4. Fibonacci
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Correct answer: C. François Viète

The sixteenth-century French mathematician Viète found this trigonometric solution independently.

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Which Persian poet-mathematician found that a cubic can have more than one solution?

  1. Bhaskara II
  2. Omar Khayyam
  3. Wang Xiaotong
  4. Diophantus
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Correct answer: B. Omar Khayyam

In the 11th century Omar Khayyam observed that a cubic equation can have more than one solution.

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Which Tang dynasty mathematician numerically solved 25 cubic equations?

  1. Menaechmus
  2. Hippocrates
  3. Wang Xiaotong
  4. Diophantus
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Correct answer: C. Wang Xiaotong

Wang Xiaotong's 7th century treatise Jigu Suanjing solved 25 cubics of the form x³ + px² + qx = N numerically.

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More Quantitative Aptitude topics

Time Value of MoneyProbabilityPermutations and CombinationsCorrelation and RegressionRatio and Proportion, Indices and LogarithmsSets, Relations and FunctionsMeasures of Central Tendency and DispersionStatistical Representation of Data and Sampling