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JEE Quadratic Equation PYQs with Solutions

38 previous year questions from Quadratic Equation (JEE Main & Advanced IOQM) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

38 questionsIOQMAnswers + solutions

About Quadratic Equation PYQs

Quadratic Equation has 38 previous year questions in the Quantrex Academy JEE Main & Advanced IOQM bank. The 38 questions in this list come from Olympiad workbook (38). Each question opens on its own page with the options, the correct answer and the worked solution where available.

JEE Quadratic Equation PYQs with Solutions

About Quadratic Equation PYQs

Quadratic Equation questions with solutions

Suppose the prime numbers p and q satisfy q^2+3 p=197 p^2+q . Write (q)/(p) as l+(m)/(n) , where l, m, n are positive integers, m < n and GCD(m, n)=1 . Find the maximum value of

Let X=\ -5,-4,-3,-2,-1,0,1,2,3,4,5\ and S=\ (a, b) ∈ X × X: x^2+a x+b. and x^3+b x+a have at least a common real zero\ . How many elements are there in S ?

If x= 2 + 3 + 6 is a root of x^4+a x^3+b x^2+c x+d=0 where a, b, c, d are integers, what is the value of |a+b+c+d| ?

Suppose that P is the polynomial of least degree with integer coefficients such that P( 7 + 5 )=2( 7 - 5 ) . Find P(2) .

Let A=\ m: m. an integer and the roots of x^2+m x + 2020 = 0 are positive integers) and B=(n: n. an integer and the roots of x^2+2020 x+ n=0 are negative integers). Suppose a is

Let x, y, z be complex numbers such that aligned & (x)/(y+z)+(y)/(z+x)+(z)/(x+y)=9 & (x^2)/(y+z)+(y^2)/(z+x)+(z^2)/(x+y)=64 & (x^3)/(y+z)+(y^3)/(z+x)+(z^3)/(x+y)=488 aligned If

Suppose a, b are positive real numbers such that a a +b b =183, a b +b a =182 . Find (9)/(5)(a+b) .

Let f(x)=x^2+a x+b . If for all nonzero real x f(x+(1)/(x))=f(x)+f((1)/(x)) and the roots of f(x)=0 are integers, what is the value of a^2+b^2 ?

Let t be the area of a regular pentagon with each side equal to 1 . Let P(x)=0 be the polynomial equation with least degree, having integer coefficients, satisfied by x=t and the

Determine the sum of all possible positive integers n , the product of whose digits equals n^2-15 n- 27.

Three positive integers a, b, c with a>c satisfy the following equations: a c+b+c=b c+a+66, a+b+c=32 . Find the value of a .

Suppose a, b are integers and a+b is a root of x^2+ax+b=0 . What is the maximum possible values of b^2 ?

Suppose an integer r , a natural number n and a prime number p satisfy the equation 7 x^2-44 x+12=p^n . Find the largest value of p .

A positive integer m has the property that m^2 is expressible in the form 4 n^2-5 n+16 where n is an integer (of any sign). Find the maximum possible value of |m-n| .

Suppose 1,2,3 are the roots of the equation x^4+a x^2+b x=c . Find the value of c .

Let a, b be integers such that all the roots of the equation (x^2+a x+20)(x^2+17 x+b)=0 are negative integers. What is the smallest possible value of a+b ?

Let a, b, c be reals satisfying 3 a b+2=6 b, 3 b c+2=5 c, 3 c a+2=4 a Let Q denote the set of all rational numbers. Given that the product a b c can take two values (r)/(s) ∈ Q

Let a, b be positive integers satisfying a^3-b^3-a b=25 . Find the largest possible value of a^2+b^3 .

Find the number of ordered triples (x, y, z) of real numbers that satisfy the system of equation : x+y+z=7 ; x^2+y^2+z^2=27 ; x y z=5