Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- If 75^ and 15^ are the roots of the quadratic equation x^2+Px+Q=0, then evaluate Q-P.
- If A and B are the roots of abx^2-c^2x+ab=0, where a,b,c are the sides of the triangle ABC, then the value of ^2A+ ^2B+ ^2C is
- The maximum value of 4 ^2x-12 x+7 is
- If p= ^2x+ ^4x, then
- If , are the roots of ax^2-bx+c=0, then
- If and cosec , are the roots of the equation x^2-px+q=0, then
- If + =1, then a root of the equation (a-2b+c)x^2+(b-2c+a)x+(c-2a+b)=0 is
- If , , are the roots of the equation x^3-px^2-r=0, then the value of (1+ ^2 )(1+ ^2 )(1+ ^2 ) is equal to
- If x a+y 2a+z 3a= 4a, x b+y 2b+z 3b= 4b and x c+y 2c+z 3c= 4c, then the roots of the equation t^3- ( z 2 )t^2- ( y+2 4 )t+ ( z-x...
- If A= ^2 + ^4 , then for all real values of
- In a triangle ABC, C= 2 . If ( A 2 ) and ( B 2 ) are the roots of the equation ax^2+bx+c=0 (a 0), then the value of a+b c is ____.
- The number of integral values of a for which the equation ^2x- x+a=0 has roots when x (0, /2) is ____.
- If ABCD is a convex quadrilateral such that 4 A+5=0, then the quadratic equation whose roots are A and cosec ,A is
- If ABCD is a cyclic quadrilateral such that 12 A-5=0 and 5 B+3=0, then the quadratic equation whose roots are C and D is
- If A= ^2 + ^4 , then for all values of
- The quadratic equation whose roots are ^2 and cosec ^2 can be
- If a,b,c denote the sides of a ABC and the equations ax^2+bx+c=0 and x^2+ 2x+1=0 have a common root, then C=
- The equation ( p-1)x^2+( p)x+ p=0, where x is a variable, has real roots. Then the interval of p may be any one of the following:
- Let and be the roots of equation px^2 + qx + r = 0, p 0. If p, q, r are in A.P. and 1 + 1 = 4, then the value of | - | is
- If a R and the equation -3(x - [x])^2 + 2(x - [x]) + a^2 = 0 (where [x] denotes the greatest integer x) has no integral solution,...
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