Mathematics questions
18011 published questions with worked solutions.
- If the cubic 2x^3-9x^2+12x+k=0 has two equal roots, then maximum value of |k| is
- Suppose a,b,c are the roots of the cubic x^3-x^2-2=0. Then the value of a^3+b^3+c^3 is
- If a,b,c are non-zero real numbers, then the minimum value of the expression ( (a^4+3a^2+1 ) (b^4+5b^2+1 ) (c^4+7c^2+1 )...
- If the equation 2x^2+4xy+7y^2-12x-2y+t=0 where t' is a parameter has exactly one real solution of the form (x,y). Then the sum of...
- Let _1, _1 are the roots of x^2-6x+p=0 and _2, _2 are the roots of x^2-54x+q=0. If _1, _1, _2, _2, from an increasing G.P., then...
- Let a,b and c be distinct non zero real numbers such that 1-a^3 a= 1-b^3 b= 1-c^3 c. The value of (a^3+b^3+c^3 ), is
- The function f(x)=ax^3+bx^2+cx+d has three positive roots. If the sum of the roots of f(x) is 4, the largest possible integral...
- Given and are the roots of the quadratic equation x^2-4x+k=0 (k 0). If , ^2+ ^2 , ^3+ ^3 are in geometric progression, then the...
- Let P(x)= 53-6x-9x^2 and Q(y)=-4y^2+4y+ 13 2. If there exist unique pair of real numbers (x,y) such that P(x)Q(y)=20, then the...
- a,b and c are all different and non-zero real numbers in arithmetic progression. If the roots of quadratic equation ax^2+bx+c=0...
- If set of values of a' for which f(x)=ax^2-(3+2a)x+6, a 0 is positive for exactly three distinct negative integral values of x...
- Polynomial P(x) contains only terms of odd degree. When P(x) is divided by (x-3), the remainder is 6. If P(x) is divided by...
- If the roots of the cubic, x^3+ax^2+bx+c=0 are three consecutive positive integers. Then the value of a^2 b+1 is equal to
- The quadratic polynomial p(x) has the following properties: p(x) 0 for all real numbers, p(1)=0 and p(2)=2. Find the value of...
- If a and b are positive numbers and each of the equations x^2+ax+2b=0 and x^2+2bx+a=0 has real roots, then the smallest possible...
- Let P(x)=x^3-8x^2+cx-d be a polynomial with real coefficients and with all its roots being distinct positive integers. Then...
- If a^2-4a+1=4, then the value of a^3-a^2+a-1 a^2-1 (a^2 1 ) is equal to
- Let x^2+y^2+xy+1 a(x+y) x,y R, then the number of possible integer(s) in the range of a is
- The quadratic equation x^2+mx+n=0 has roots which are twice those of x^2+px+m=0 and m,n and p 0. Then the value n/p is
- If the equation x^2+2( +1)x+ ^2+ +7=0 has only negative roots, then the least value of equals