Quadratic equations CAT problems consists of important quadratic equations questions for CAT. This CAT questions will be very useful for quantitative aptitude for CAT.<\/p>\n
Taking a free CAT mock test<\/a> and solving CAT past papers<\/a> will definitely help you to get good understanding of the simple, linear and quadratic equations CAT questions.<\/p>\n You can download the\u00a0Quadratic Equations CAT Problems or you can go through the details below.<\/p>\n Download\u00a0Quadratic Equations CAT Problems PDF<\/a><\/p>\n 6 Months Intensive Course @ Just Rs. 7999<\/a><\/p>\n Quadratic Equations CAT Problems:<\/strong><\/p>\n Question 1:<\/strong><\/p>\n Given the quadratic equation $x^2 \u2013 (A \u2013 3)x \u2013 (A \u2013 2)$, for what value of $A$ will the sum of the squares of the roots be zero?<\/p>\n A.\u00a0<\/strong>-2<\/p>\n B.\u00a0<\/strong>3<\/p>\n C.\u00a0<\/strong>6<\/p>\n D.\u00a0<\/strong>None of these<\/p>\n Question 2:<\/strong><\/p>\n The roots of the equation $ax^{2} + 3x + 6 = 0$ will be reciprocal to each other if the value of a is<\/p>\n A.\u00a0<\/strong>3<\/p>\n B.\u00a0<\/strong>4<\/p>\n C.\u00a0<\/strong>5<\/p>\n D.\u00a0<\/strong>6<\/p>\n Question 3:<\/strong><\/p>\n A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f (x) at x = 10?<\/p>\n A. <\/strong>-119<\/p>\n B. <\/strong>-159<\/p>\n C. <\/strong>-110<\/p>\n D. <\/strong>-180<\/p>\n Question 4:<\/strong><\/p>\n If the roots of the equation $x^3 \u2013 ax^2 + bx \u2013 c = 0$ are three consecutive integers, then what is the smallest possible value of b?<\/p>\n A.\u00a0<\/strong>$\\frac{-1}{\\sqrt 3}$<\/p>\n B.\u00a0<\/strong>-1<\/p>\n C.\u00a0<\/strong>0<\/p>\n D.\u00a0<\/strong>1<\/p>\n Question 5:<\/strong><\/p>\n If $xy + yz + zx = 0$, then $(x + y + z)^2$ equals<\/p>\n A.\u00a0<\/strong>$(x + y)^2 + xz$<\/p>\n B.\u00a0<\/strong>$(x + z)^2 + xy$<\/p>\n C.\u00a0<\/strong>$x^2 + y^2 + z^2$<\/p>\n D.\u00a0<\/strong>$2(xy + yz + xz)$<\/p>\n Download CAT Quantitative Aptitude Questions PDF<\/a><\/p>\n Take a free mock test for CAT<\/a><\/p>\n Solutions:<\/strong><\/p>\n 1)<\/strong> Answer (D)<\/p>\n For summation of square of roots to be zero, individual roots should be zero. Hence summation should be zero i.e. \u00a0A-3=0 ; A = 3 And product of roots will also be zero i.e. A-2 = 0 ; A =2 So there is no unique value of A which can satisfy above equation.<\/p>\n 2)<\/strong> Answer (D)<\/p>\n If roots of given equation are reciprocal to each other than product of roots should be equal to 1. 3)<\/strong> Answer (B)<\/p>\n Let the function be $ax^2 + bx + c$. 4)<\/strong> Answer (B)<\/p>\n b = sum of the roots taken 2 at a time. 5)<\/strong> Answer (C)<\/p>\n $(x+y+z)^2 = x^2 + y^2 + z^2 + 2(xy + yz + xz)$ Hope you will find this quadratic equations CAT Problems useful, you can also download all our CAT Verbal Ability PDF’s<\/a>.<\/p>\n
\ni.e. $\\frac{6}{a} = 1$
\nhence a=6<\/p>\n
\nWe know that x=0 value is 1 so c=1.
\nSo equation is $ax^2 + bx + 1$.
\nNow max value is 3 at x = 1.
\nSo after substituting we get a + b = 2.
\nIf f(x) attains a maximum at ‘a’ then the differential of f(x) at x=a, that is, f'(a)=0.
\nSo in this question f'(1)=0
\n=> 2*(1)*a+b = 0
\n=> 2a+b = 0.
\nSolving the equations we get a=-2 and b=4.
\n$ -2x^2 + 4x + 1$ is the equation and on substituting x=10, we get -159.<\/p>\n
\nLet the roots be n-1, n and n+1.
\nTherefore, $b = (n-1)n + n(n+1) + (n+1)(n-1) = n^2 – n + n^2 + n + n^2 – 1$
\n$b = 3n^2 – 1$. The smallest value is -1.<\/p>\n
\nas $xy+yz+xz = 0$
\nso equation will be resolved to $x^2 + y^2 + z^2$<\/p>\n