CAT Quadratic equations & expressions Questions

Quadratic equations contain a squared variable and can be studied through factorisation, roots or a parabola. Quadratic expressions also describe maximum or minimum values under appropriate conditions.

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Key concepts

• Discriminant and the nature of roots
• Sum and product of roots
• Completing the square and the vertex

CAT quadratic equations & expressions practice questions

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Common mistakes

• Dropping one root after taking a square root.
• Ignoring restrictions inherited from the original problem.

Practical solving approaches

• Try factorisation before using the quadratic formula.
• Use completing the square for extrema and substitute possible roots into the original equation.

Quadratic equations & expressions FAQs

What does the discriminant tell me?

For real coefficients, a positive discriminant gives two distinct real roots, zero gives a repeated real root, and a negative discriminant gives no real roots.

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CAT Quadratic equations & expressions Questions

Quadratic equations contain a squared variable and can be studied through factorisation, roots or a parabola. Quadratic expressions also describe maximum or minimum values under appropriate conditions.

3 free practice questions

Key concepts

• Discriminant and the nature of roots
• Sum and product of roots
• Completing the square and the vertex

CAT quadratic equations & expressions practice questions

Question 1Multiple choiceMEDIUM

Question 1

Select the correct alternative from the given choices.

Each question is followed by two statements, A and B. Answer each question using the following instructions.
Choose [1], if the question can be answered by one of the statements alone but not by the other.
Choose [2], if the question can be answered by using either statement alone.
Choose [3], if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
Choose [4], if the question cannot be answered even by using both the statements together.

What are the unique values of b and c in the question 4x² + bx + c = 0 if one of the roots of the equation is (–1/2) ?

A. The second root is 1/2.
B. The ratio of c and b is 1.

Choose an answer

A.1B.2C.3D.4

Check answerView solution

Question 2Multiple choiceEASY

Question 2

Select the correct alternative from the given choices.

Answer the questions independently of each other.

The ratio of A.M. of 'a' and 'b' to their G.M. is m : n. What is the value of a : b?

Choose an answer

A.

B.

C.

D.

Check answerView solution

Question 3Multiple choiceHARD

Question 3

Select the correct alternative from the given choices.

There are 500 rooms in a multi-floored hotel. However, due to a change in rule, the hotel has to decrease the number of floors by 5. However, the management is able to put 5 more rooms on each floor. Over all, the number of rooms in the hotel decreases by 10%. Find the number of floors and the number of rooms/floor the hotel originally had?

 

Choose an answer

A.10 floors 50 rooms B.20 floors 20 rooms C.20 floors 25 rooms D.50 floors 10 rooms

Check answerView solution

Common mistakes

• Dropping one root after taking a square root.
• Ignoring restrictions inherited from the original problem.

Practical solving approaches

• Try factorisation before using the quadratic formula.
• Use completing the square for extrema and substitute possible roots into the original equation.

Quadratic equations & expressions FAQs

What does the discriminant tell me?

For real coefficients, a positive discriminant gives two distinct real roots, zero gives a repeated real root, and a negative discriminant gives no real roots.

More Algebra practice

• Functions & graphs →
• Inequalities & modulus →
• Linear equations & word problems →
• Logarithms, indices & surds →
• Polynomials, higher-degree equations & binomial expansion →
• Sequences & series →