Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- If the sum of the squares of the roots of the equation x^2-(a-2)x-(a+1)=0 is least, then the value of a is
- The value of m for which the equation x^3-mx^2+3x-2=0 has two roots equal in magnitude but opposite in sign, is
- The value of k for which the equation (k-2)x^2+8x+k+4=0 has both roots real, distinct and negative, is
- If the sum of the squares of the roots of the equation x^2-( -2)x-(1+ )=0 is least, then =
- The value of k' for which one of the roots of x^2-x+3k=0, is double of one of the roots of x^2-x+k=0 is
- The quadratic equations x^2+ (a^2-2 )x-2a^2=0 and x^2-3x+2=0 have
- The value of p for which both the roots of the equation 4x^2-20px+ (25p^2+15p-66 )=0 are less than 2, lies in
- Let x_1,x_2 be the roots of the equation x^2-3x+p=0 and let x_3,x_4 be the roots of the equation x^2-12x+q=0. If the numbers...
- If the roots of ax^2-bx-c=0 change by the same quantity, then the expression in a,b,c that does not change is
- If the sum of the roots of the equation (a+1)x^2+(2a+3)x+(3a+4)=0 is -1, then the product of the roots is
- If one root of the equation 5x^2+13x+k=0 is reciprocal of other, then the value of k is
- If the expressions x^2-11x+a and x^2-14x+2a have a common root, then the values of a' is
- If the equations ax^2+bx+c=0 and 2x^2+3x+4=0 have a common root, then a:b:c
- The number of real roots of the equation (x-1)^2+(x-2)^2+(x-3)^2=0 is
- If m Z and the equation mx^2+(2m-1)x+(m-2)=0 has rational roots, then m is of the form
- If roots of ax^2+bx+c=0, a,b,c R, a 0 are imaginary then
- Let S denote the set of all real values of a for which the roots of the equation x^2-2ax+a^2-1=0 lie between 5 and 10, then S...
- The set of values of a' for which x^2+ax+ ^ -1 (x^2-4x+5 )+ ^ -1 (x^2-4x+5 )=0 has at least one real root is given by
- If the equation 2x^2-7x+1=0 and ax^2+bx+2=0 have a common root, then
- The equation (x-b)(x-c)+(x-a)(x-b)+(x-a)(x-c)=0 has all its roots
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