Quadratic Equations and Inequalities questions
963 published questions with worked solutions.
- Two students while solving a quadratic equation in x, one copied the constant term incorrectly and got the roots 3 and 2. The...
- One lies between the roots of the equation -x^2+ax+a=0, a R if and only if a lies in the interval
- If x^2+2ax+b c, x R, then
- If the roots of the equation x^2-2ax+a^2+a-3=0 are real and less than 3, then
- Suppose the quadratic equations x^2+px+q=0 and x^2+rx+s=0 are such that p,q,r,s are real and pr=2(q+s). Then
- If the roots of (a^2+b^2 )x^2-2(bc+ad)x+c^2+d^2=0 are equal, then
- If one root of the equation x^2- x+12=0 is even prime while x^2+ x+ =0 has equal roots, then is
- If the equation x^2+9y^2-4x+3=0 is satisfied values of x and y, then
- If roots of the equation (a-b)x^2+(c-a)x+(b-c)=0 are equal, then a,b,c are in
- If the roots of the equation (p^2+q^2 )x^2-2q(p+r)x+ (q^2+r^2 )=0 be real and equal, then p,q,r will be in
- If the equation ax^2+2bx-3c=0 has non-real roots and 3c 4<a+b, then c is
- In the equation a_4x^4+a_3x^3+a_2x^2+a_1x+a_0=0 roots of the equation are _i, i=1,2,3,4. Now, x is replaced by x-1, now roots of...
- In writing an equation of the form ax^2+bx+c=0; the coefficient of x is written incorrectly and roots are found to be equal....
- If a root of the equation ax^2+bx+c=0 be reciprocal of a root of the equation a'x^2+b'x+c'=0, then
- If , , are the roots of the equation x^3-7x+7=0, then 1 ^4 + 1 ^4 + 1 ^4 is
- Rational roots of the equation 2x^4+x^3-11x^2+x+2=0 are
- The value of a for which the equations x^3+ax+1=0 and x^4+ax^2+1=0 have a common root, is
- If 2 ^2 8 is a root of the equation x^2+ax+b=0, where a and b are rational numbers, then a-b is equal to
- Consider the following statements: 1. The equation x^2-cx+d=0 and x^2-ax+b=0 have common root and second equation has equal roots...
- The number of real roots of the equation e^ x -e^ - x -4=0 are
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