Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- If a, a_1, a_2, a_3, , a_ 2n-1 , b are in AP, a, b_1, b_2, b_3, , b_ 2n-1 , b are in GP and a, c_1, c_2, c_3, , c_ 2n-1 , b are...
- The number of real solutions of x- 1 x^2-4 =2- 1 x^2-4 is
- The number of values of the pair (a,b) for which a(x+1)^2+b(x^2-3x-2)+x+1=0 is an identity in x is
- The polynomial (ax^2+bx+c)(ax^2-dx-c), ac 0, has
- The sum of the real roots of the equation x^2+|x|-6=0 is
- The product of all the solutions of the equation (x-2)^2-3|x-2|+2=0 is
- The number of real solutions of the equation 6-x x^2-4 =2+ x x+2 is
- If [x]= the greatest integer less than or equal to x, and (x)= the least integer greater than or equal to x, and [x]^2+(x)^2>25...
- If x Z (the set of integers) such that x^2-3x<4 then the number of possible values of x is
- If a,b,c are nonzero, unequal rational numbers then the roots of the equation abc^2x^2+(3a^2+b^2)cx-6a^2-ab+2b^2=0 are
- If l,m are real and l m then the roots of the equation (l-m)x^2-5(l+m)x-2(l-m)=0 are
- If a,b,c,d are four consecutive terms of an increasing AP then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 are
- If a,b,c are three distinct positive real numbers then the number of real roots of ax^2+2b|x|-c=0 is
- The equation x^2-6x+8+ (x^2-4x+3)=0, R, has
- If , , are in GP then roots of x^2+2 x+1=0 are always
- The roots of ax^2+bx+c=0, where a 0 and coefficients are real, are nonreal complex and a+c<b. Then
- If a 3^ x +a 3^ - x -2=0 has real solutions, x 2 , 0 x , then the set of possible values of the parameter a is
- If a>1, roots of the equation (1-a)x^2+3ax-1=0 are
- If a R , b R then the equation x^2-abx-a^2=0 has
- If , be the roots of 4x^2-16x+ =0, R such that 1< <2 and 2< <3 then the number of integral solutions of is
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