Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- The numbers of pairs (a, b) of real numbers, such that whenever is a root of the equation x^2+ax+b=0, ^2-2 is also a root of this...
- Let P(x) = x^2 + bx + c be a quadratic polynomial with real coefficients such that _0^1P(x)dx=1 and P(x) leaves remainder 5 when...
- If and are the distinct roots of the equation x^2+(3)^ 1/4 x+3^ 1/2 =0, then the value of ^ 96 ( ^ 12 -1)+ ^ 96 ( ^ 12 -1) is...
- The probability of selecting integers a [–5,30] such that x^2+2(a+4)x-5a+64>0, for all x R is
- Let p and q be two positive numbers such that p + q = 2 and p^4+q^4=272. Then p and q are roots of the equation :
- Degree of the polynomial [ x^2+1 + x^2-1 ]^8+ [ 1 x^2+1 + x^2-1 ]^8 is
- If a,b,c,d and p are distinct real numbers such that (a^2+b^2+c^2 )p^2-2(ab+bc+cd)p+ (b^2+c^2+d^2 ) 0, then
- If p,q,r are in AP and are positive, the roots of the quadratic equation px^2+qx+r=0 are all real for
- If the AM and GM of roots of a quadratic equations are 8 and 5 respectively, then the quadratic equation will be
- If positive numbers a^ -1 ,b^ -1 ,c^ -1 are in AP, then the product of roots of the equation x^2-kx+2b^ 101 -a^ 101 -c^ 101 =0,...
- , are the roots of the equation x^2-3x+a=0. , are the roots of x^2-12x+b=0. If , , , form an increasing GP, then (a,b) is equal to
- Let a,p,q,r,s R 0 . If 3a^2+2 ( 1p- 1s )a+ 1 p^2 + 1 q^2 + 1 r^2 -2 ( 1 pq + 1 qr + 1 rs ) 0 for some real a, then p,q,r,s are in
- The coefficient of the quadratic equation ax^2+(a+d)x+(a+2d)=0 are consecutive terms of a positively valued, increasing...
- If the equation x^3+ax^2+bx+216=0 has three real roots in G.P., then b/a has the equal to
- If d,e,f are in G.P. and the two quadratic equations ax^2+2bx+c=0 and dx^2+2ex+f=0 have a common root, then
- Let p and q be the roots of x^2-3x+m=0 and r and s be the roots of x^2-23x+n=0. If p<q<r<s are in A.P., then find the value of...
- Let a,b,c R. If f(x)=ax^2+bx+c is such that 2 +2 =-2 and = 12, then =- 32 is equal to
- Let a,b be two non-zero real numbers. If p and r are the roots of the equation x^2-8ax+2a=0 and q and s are the roots of the...
- For p,q R, consider the real valued function f(x)=(x-p)^2-q, x R and q>0. Let a_1,a_2,a_3 and a_4 be in an arithmetic progression...
- Let , be two roots of the equation x^2+(20)^ 1/4 x+(5)^ 1/2 =0. Then ^8+ ^8 is equal to
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