Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- A value of b for which the equations x^2 + bx - 1 = 0 x^2 + x + b = 0, have one root in common is
- The quadratic equation p(x) = 0 with real coefficients has purely imaginary roots. Then the equation p(p(x)) = 0 has
- Let S be the set of all non-zero real numbers such that the quadratic equation x^2-x+ =0 has two distinct real roots x_1 and x_2...
- Let - 6 < <- 12 . Suppose _1 and _1 are the roots of the equation x^2-2x +1=0 and _2 and _2 are the roots of the equation x^2+2x...
- If , are the roots of the equation x^2 + px + q = 0 (p 0), then
- The probability of choosing randomly a number c from the set 1, 2, 3, , 9 such that the quadratic equation x^2 + 4x + c = 0 has...
- The value of f(x) = 2x^2 - 3x + 4 at x = 7 and x = -2t are
- If c>0 and 4a+c<2b, then ax^2-bx+c=0 has a root in which one of the following intervals?
- If A= x R : x^2+6x-7<0 and B= x R : x^2+9x+14>0 , then which of the following is/are correct? 1. A B= x R : -2<x<1 2. A B= x R :...
- If both the roots of the equation x^2-2kx+k^2-4=0 lie between -3 and 5, then which one of the following is correct?
- If the difference between the roots of the equation x^2+kx+1=0 is strictly less than 5 , where |k| 2, then k can be any element...
- If the roots of the equation x^2+px+q=0 are in the same ratio as those of the equation x^2+lx+m=0, then which one of the...
- If the graph of a quadratic polynomial lies entirely above x-axis, then which one of the following is correct?
- If and are the roots of the equation x^2+bx+c=0 with b 0, then the value of ( + ) is
- The sum of the roots of the equation x^2+bx+c=0 (where b and c are non-zero) is equal to the sum of the reciprocals of their...
- The sum of the roots of the equation ax^2+x+c=0 (where a and c are non-zero) is equal to the sum of the reciprocals of their...
- The roots of the equation (q-r)x^2+(r-p)x+(p-q)=0 are
- It is given that the roots of the equation x^2-4x- _3P=0 are real. For this, the minimum value of P is
- If and are the roots of the equation 3x^2+2x+1=0, then the equation whose roots are + ^ -1 and + ^ -1 is
- In PQR, R= 2 . If ( P 2 ) and ( Q 2 ) are the roots of the equation ax^2+bx+c=0, then which one of the following is correct?
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