Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- If , are the roots of the equation ax^2+bx+c=0 such that < <0, then the quadratic equation whose roots are | |,| |, is given by
- The solution of the quadratic equation (3|x|-3)^2=|x|+7 which belongs to the domain of definition of the function y= x(x-3) are...
- If the roots of the equation 1 x+p + 1 x+q = 1r are equal in magnitude but opposite in sign, then the product of the roots will be
- If a>0,b>0,c>0, then both the roots of the equation ax^2+bx+c=0
- If and be the roots of x^2+px+q=0, then ( + ^2 ) ( ^2 + ) ^2 + ^2 is equal to
- If the product of the roots of the equation (a+1)x^2+(2a+3)x+(3a+4)=0 is 2, then the sum of roots is
- If at least one root of 2x^2+3x+5=0 and ax^2+bx+c=0, a,b,c N is common, then the maximum value of a+b+c is
- Let , be the roots of the equation ax^2+2bx+c=0 and , be the roots of the equation px^2+2qx+r=0. If , , , are in GP, then
- Let a,b,c,p,q be real numbers. Suppose , are the roots of the equation x^2+2px+q=0 and , 1 are the roots of the equation...
- Let and be the solutions of the quadratic equation x^2-1154x+1=0, then the value of [4] + [4] is equal to
- f:R R, f(x)= 3x^2+mx+n x^2+1 . If the range of this function is [-4,3], then find the value of |m+n| is
- Suppose a,b,c I such that greatest common divisor of x^2+ax+b and x^2+bx+c is (x+1) and the least common multiple of x^2+ax+b and...
- 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 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...
- 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...
- 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...
- 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
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