Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- 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...
- Let and be the roots of equation x^2-6x-2=0. If a_n= ^n- ^n for n 1, then the value of a_ 10 -2a_8 2a_9 is
- The quadratic equation p(x)=0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has
- Let and be the roots of equation px^2+qx+r=0, p 0. If p,q and r are in A.P. and 1 + 1 =4, then the value of | - | is
- The set of all real numbers x for which x^2-|x+2|+x>0 is
- If the equations x^2+2x+3=0 and ax^2+bx+c=0, a,b,c R have a common root, then a:b:c is
- A value of b for which the equations x^2+bx-1=0 and x^2+x+b=0 have one root in common is
- Let , be the roots of the equation (x-a)(x-b)=c, c 0. Then the roots of the equation (x- )(x- )+c=0 are
- 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, then...
- If and are the roots of the equation x^2-5x+1=0, then find the value of 1 ( -5)^2 + 1 ( -5)^2 .
- Find the sum of the roots of the equation 2 (x^2+ 1 x^2 )-9 (x+ 1x )+14=0, x R.
- Find the number of all possible positive integral values of for which the roots of 7x^2-15x+ =0 are rational numbers.
- If the product of the roots of ax^2+bx+c=0 is 9 and a,b,c are in A.P., then find the sum of its roots.
- If and are the roots of the equation x^2-a(x+1)-b=0, then find the value of ^2+2 +1 ^2+2 +b + ^2+2 +1 ^2+2 +b .
- Let a,b 1,2,3,4,5 . Find the number of equations of the form ax^2+bx+1=0 having real roots.
- If and are the roots of the equation 6x^2+11x+3=0, then find the value of (6 +11)^2+(6 +11)^2.
- If the roots of the equation x^2+ 3ax-b=0 are 15^ and 45^ , then find the value of 7+a+b.
- If r and s are the roots of the equation x^2-10px-11q=0 and p and q are the roots of the equation x^2-10rx-11s=0, then find the...
- Let f(x)=ax^2+bx+c, where a,b,c are real constants and a 0. If f(13)=-8f(3) and f(-7)=0, then find the value of f(5).
- If and are the roots of the equation x^2-4x-1=0, find ^5+ ^5.
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