Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- The values of k for which the equations x^2-kx-21=0 and x^2-3kx+35=0 will have a common roots are
- If 3x (x-a)(x-b) = 2 x-a + 1 x-b , then a:b is equal to
- Given that the equation z^2+(p+iq)z+r+is=0, where p,q,r,s are real and non-zero has real roots, then
- For all x', x^2+2ax+(10-3a)>0, then the interval in which a' lies, is
- Statement 1: The greatest integral value of for which (2 -1)x^2-4x+(2 -1)=0 has real roots, is 2. Statement 2: For real roots of...
- Statement 1: If a+b+c=0 and a,b,c are rational, then the roots of the equation (b+c-a)x^2+(c+a-b)x+(a+b-c)=0 are rational....
- If a<b<c<d, then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 are
- If the roots of the equation x^2+px+q=0 are and and roots of the equation x^2-xr+s=0 are ^4, ^4, then the roots of the equation...
- If at least one root of the equation x^3+ax^2+bx+c=0 remains unchanged, when a,b and c are decreased by one, then which one of...
- Statement 1: Let f(x) be quadratic expression such that f(0)+f(1)=0. If -2 is one of the root of f(x)=0, then other root is 35....
- If the expression (mx-1+ 1x ) is always non-negative, then the minimum value of m must be
- If the roots of the equation x- + x- =1 be equal in magnitude but opposite in sign, then + is equal to
- If and be the roots of the equation x^2+x + =0, then
- and are the roots of the equation x^2+ax+b=0, then the value of ^2( + )+a ( + ) ( + )+b ^2( + ) is equal to
- Let f(x)=x^2+ax+b; a,b R. If f(1)+f(2)+f(3)=0, then the roots of the equation f(x)=0
- The least value of |a| for which and are roots of the equation x^2+ax+1=0, is
- If x^2+2x+2xy+my-3 has two rational factors, then the values of m will be
- If and are the roots of ax^2+bx+c=0, then the equation ax^2-bx(x-1)+c(x-1)^2=0 has roots
- If the equation ax^2+2bx+3c=0 and 3x^2+8x+15=0 have a common root, where a,b,c are the lengths of the sides of a ABC, then ^2A+...
- Number of real roots of the equation (6-x)^4+(8-x)^4=16 is
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