Daily Quiz
Quantitative Aptitude — Polynomials and Linear Equations
← All Quizzes Home

Quantitative Aptitude — Polynomials and Linear Equations

⏱
15 mins
Time
❓
20
Questions
🎓
1
Per Q

Read the following instructions carefully:

✡ Select Language / भाषा चुनें
You can change language during quiz too / परीक्षा के दौरान भी बदल सकते हैं
Quantitative Aptitude — Polynomials and Linear Equations — Questions with Answers Open after you finish the quiz — all 20 questions, with answers and explanations.
Q1. Find the zeroes of the quadratic polynomial x^2 - 5x + 6.
  1. 2, 3
  2. -2, -3
  3. 1, 6
  4. -1, -6
Show answer
Answer: A. 2, 3
To find the zeroes, set the polynomial to zero: x^2 - 5x + 6 = 0. Factor the quadratic: (x-2)(x-3) = 0. So, x=2 or x=3.
Q2. What is the zero of the linear polynomial 2x + 4?
  1. 2
  2. -2
  3. 4
  4. -4
Show answer
Answer: B. -2
To find the zero, set the polynomial to zero: 2x + 4 = 0. Subtract 4 from both sides: 2x = -4. Divide by 2: x = -2.
Q3. A polynomial of degree 'n' can have at most how many zeroes?
  1. n-1
  2. n+1
  3. n
  4. 2n
Show answer
Answer: C. n
According to the Fundamental Theorem of Algebra, a polynomial of degree 'n' has exactly 'n' roots (counting multiplicity) in the complex numbers. For real zeroes, it can have at most 'n' zeroes.
Q4. Geometrically, what do the zeroes of a polynomial represent on its graph?
  1. y-intercepts
  2. Turning points
  3. Vertices
  4. x-intercepts
Show answer
Answer: D. x-intercepts
The zeroes of a polynomial are the values of x for which the polynomial evaluates to zero. On a graph, these are the points where the graph intersects the x-axis, also known as x-intercepts.
Q5. Based on the pie chart, which type of polynomial is most represented?
  1. Linear
  2. Quadratic
  3. Cubic
  4. Biquadratic
Show answer
Answer: B. Quadratic
The pie chart shows Quadratic polynomials at 35%, which is the highest percentage among the given types.
Q6. For a quadratic polynomial ax^2 + bx + c, what is the sum of its zeroes?
  1. -b/a
  2. c/a
  3. b/a
  4. -c/a
Show answer
Answer: A. -b/a
For a quadratic polynomial ax^2 + bx + c, the sum of its zeroes is given by the formula -b/a.
Q7. Form a quadratic polynomial whose zeroes are 2 and 3.
  1. x^2 + 5x + 6
  2. x^2 - 5x + 6
  3. x^2 - x - 6
  4. x^2 + x - 6
Show answer
Answer: B. x^2 - 5x + 6
If zeroes are α and β, the polynomial is k(x^2 - (α+β)x + αβ). Here α=2, β=3. Sum = 2+3=5. Product = 2*3=6. So, the polynomial is x^2 - 5x + 6 (taking k=1).
Q8. For the quadratic polynomial x^2 - 3x + 2, what are the sum and product of its zeroes?
  1. Sum = -3, Product = 2
  2. Sum = 3, Product = -2
  3. Sum = 3, Product = 2
  4. Sum = -3, Product = -2
Show answer
Answer: C. Sum = 3, Product = 2
For x^2 - 3x + 2, a=1, b=-3, c=2. Sum of zeroes = -b/a = -(-3)/1 = 3. Product of zeroes = c/a = 2/1 = 2.
Q9. Find a quadratic polynomial whose sum of zeroes is 5 and product of zeroes is 6.
  1. x^2 + 5x + 6
  2. x^2 + 6x + 5
  3. x^2 - 6x + 5
  4. x^2 - 5x + 6
Show answer
Answer: D. x^2 - 5x + 6
A quadratic polynomial can be written as x^2 - (sum of zeroes)x + (product of zeroes). Given sum = 5 and product = 6, the polynomial is x^2 - 5x + 6.
Q10. What is the product of the zeroes of the polynomial 3x^2 + 5x - 2?
  1. -2/3
  2. 5/3
  3. 2/3
  4. -5/3
Show answer
Answer: A. -2/3
For a quadratic polynomial ax^2 + bx + c, the product of its zeroes is given by the formula c/a. Here, a=3, b=5, c=-2. So, product = -2/3.
Q11. When x^3 - 3x^2 + 5x - 3 is divided by x^2 - 2, what is the quotient?
  1. x+3
  2. x-3
  3. x-2
  4. x+2
Show answer
Answer: B. x-3
Using polynomial long division: (x^3 - 3x^2 + 5x - 3) / (x^2 - 2). The quotient is x-3 and the remainder is 7x-9.
Q12. According to the Division Algorithm for Polynomials, if p(x) is divided by g(x) (where g(x) ≠ 0) to get quotient q(x) and remainder r(x), which condition must r(x) satisfy?
  1. deg r(x) > deg g(x)
  2. deg r(x) = deg g(x)
  3. deg r(x) < deg g(x) or r(x) = 0
  4. r(x) = 0 only
Show answer
Answer: C. deg r(x) < deg g(x) or r(x) = 0
The Division Algorithm states that for any polynomials p(x) and g(x) with g(x) ≠ 0, there exist unique polynomials q(x) and r(x) such that p(x) = g(x)q(x) + r(x), where r(x) = 0 or deg r(x) < deg g(x).
Q13. Find the quotient when x^4 - 3x^2 - 4 is divided by x + 2.
  1. x^3 + 2x^2 + x + 2
  2. x^3 - 2x^2 - x + 2
  3. x^3 + 2x^2 - x - 2
  4. x^3 - 2x^2 + x - 2
Show answer
Answer: D. x^3 - 2x^2 + x - 2
Using synthetic division or long division for (x^4 + 0x^3 - 3x^2 + 0x - 4) / (x + 2). The quotient is x^3 - 2x^2 + x - 2 and the remainder is 0.
Q14. Based on the bar chart, how many problems involve polynomials of Degree 2?
  1. 8
  2. 4
  3. 5
  4. 3
Show answer
Answer: A. 8
The bar chart shows that 'Degree2' has a value of 8, indicating 8 problems involve polynomials of Degree 2.
Q15. Solve the pair of linear equations 2x + 3y = 11 and 2x - 4y = -24 using the substitution method.
  1. x=5, y=-2
  2. x=-2, y=5
  3. x=2, y=-5
  4. x=-5, y=2
Show answer
Answer: B. x=-2, y=5
From 2x + 3y = 11, express 2x = 11 - 3y. Substitute this into the second equation: (11 - 3y) - 4y = -24. This simplifies to 11 - 7y = -24, so -7y = -35, which means y = 5. Substitute y=5 back into 2x = 11 - 3(5) => 2x = 11 - 15 => 2x = -4 => x = -2.
Q16. Solve the pair of linear equations 3x + 4y = 10 and 4x - 3y = 5 using the elimination method.
  1. x=1, y=2
  2. x=-2, y=1
  3. x=2, y=1
  4. x=1, y=-2
Show answer
Answer: C. x=2, y=1
Multiply the first equation by 3 and the second by 4: (9x + 12y = 30) and (16x - 12y = 20). Add the two new equations: 25x = 50, so x = 2. Substitute x=2 into 3x + 4y = 10: 3(2) + 4y = 10 => 6 + 4y = 10 => 4y = 4 => y = 1.
Q17. For a pair of linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, what is the condition for a unique solution using the cross-multiplication method?
  1. a1/a2 = b1/b2 = c1/c2
  2. a1/a2 = b1/b2 ≠ c1/c2
  3. a1/a2 ≠ b1/b2 = c1/c2
  4. a1/a2 ≠ b1/b2
Show answer
Answer: D. a1/a2 ≠ b1/b2
For a unique solution, the lines represented by the equations must intersect at exactly one point. This occurs when the ratio of the coefficients of x is not equal to the ratio of the coefficients of y, i.e., a1/a2 ≠ b1/b2.
Q18. According to the line chart, what percentage of solutions for pairs of linear equations are consistent and unique?
  1. 60%
  2. 25%
  3. 15%
  4. 50%
Show answer
Answer: A. 60%
The line chart explicitly states that 'consistent unique' solutions account for 60% of the solutions.
Q19. What does it mean graphically when a pair of linear equations has no solution?
  1. The lines intersect at a single point.
  2. The lines are parallel and distinct.
  3. The lines are coincident (overlap).
  4. The lines form a right angle.
Show answer
Answer: B. The lines are parallel and distinct.
If a pair of linear equations has no solution, it means there is no common point that satisfies both equations. Graphically, this is represented by two parallel and distinct lines that never intersect.
Q20. What does it mean graphically when a pair of linear equations has infinitely many solutions?
  1. The lines intersect at a single point.
  2. The lines are parallel and distinct.
  3. The lines are coincident (overlap).
  4. The lines are perpendicular.
Show answer
Answer: C. The lines are coincident (overlap).
If a pair of linear equations has infinitely many solutions, it means every point on one line is also on the other line. Graphically, this is represented by two coincident lines, meaning they overlap completely.
More practice: today's quiz · daily current affairs · full mock tests