Given below are two statements:
Statement I : If the roots of a quadratic equation are 2 and 3, then the equation is $$x^{2} - 5x- 6 = 0$$
Statement II: If the roots of $$4x^{2}+3kx + 9 = 0$$ are real and distinct, then $$k \leq - 4$$ or $$k \geq 4$$
In the light of the above statements, choose the most appropriate answer from the options given below:
CMAT Quadratic Equations Questions
Statement 1:
k$$(x-2)(x-3)$$ = k($$x^2-5x+6$$) is the quadratic equation whose roots are 2 and 3.
Therefore, statement 1 is incorrect.
Statement 2:
Given equation: $$4x^{2}+3kx + 9 = 0$$
Roots of the equation are real and distinct when the discriminant of equation is greater than zero.
$$\left(3k\right)^2-\left(4\right)\left(4\right)\left(9\right)>0$$
$$\left(k-4\right)\left(k+4\right)>0$$
k < -4 and k > 4
But in the given statement, equal to sign is also considered which is incorrect.
If discriminant is equal to zero, roots of the equation are equal.
Therefore, statement 2 is incorrect.
The answer is option B.
Frequently Asked Questions
Yes, Quadratic Equations is an important topic in the Quantitative Aptitude section of CMAT. It tests a candidate's algebraic knowledge, problem-solving skills, and ability to solve equation-based questions efficiently.
The number of Quadratic Equations questions varies from year to year. CMAT does not prescribe a fixed number of questions from any specific Quantitative Aptitude topic.
CMAT may include questions on solving quadratic equations, factorization, finding roots, comparing values, identifying the nature of roots, and applying algebraic concepts to numerical problems.
Learn the fundamental concepts of quadratic equations, practice different solving methods such as factorization and algebraic techniques, revise important formulas, and solve previous year questions and mock tests regularly.
Most Quadratic Equations questions in CMAT are of easy to moderate difficulty. With conceptual clarity and regular practice, candidates can solve them accurately and efficiently.
Cracku's CMAT Quadratic Equations Questions provide topic-wise practice, detailed solutions, and exam-oriented problems that help candidates strengthen algebraic concepts, improve accuracy, and perform better in CMAT 2027.