Mathematics questions
18011 published questions with worked solutions.
- The roots of the equation _2 (x^2-4x+5 )=(x-2) are
- If a,b,c are positive real numbers, then the number of real roots of the equation ax^2+b|x|+c=0 is
- If the roots of the equation 1 x+a + 1 x+b = 1c are equal in magnitude but opposite in sign, then their product is
- If , and are the roots of x^3+8=0, then the equation whose roots are ^2, ^2 and ^2 is
- If the roots of the equation x^3+bx^2+3x-1=0 form a non-decreasing H.P., then
- If , and are the roots of x^2+qx+r=0, then + is
- If (x-1)^3 is a factor of x^4+ax^3+bx^2+cx-1, then the other factor is
- If 7^ _7 (x^2-4x+5 ) =x-1, x may have values
- If and are the roots of the equation x^2+px+q=0 with p 0, then
- If , , are the roots of the equation x^3+ax^2+bx+c=0, then ^ -1 + ^ -1 + ^ -1 =
- If two equations a_1x^2+b_1x+c_1=0 and a_2x^2+b_2x+c_2=0 have a common root, then the value of (a_1b_2-a_2b_1)(b_1c_2-b_2c_1), is
- If a,b,c R and the equations ax^2+bx+c=0 and x^3+3x^2+3x+2=0 have two roots in common, then
- The equation (a+2)x^2+(a-3)x=2a-1, a -2 has rational roots for
- If 8,2 are the roots of x^2+ax+ =0, and 3,3 are the roots of x^2+ x+b=0, then the roots of x^2+ax+b=0 are
- If , are the roots of x^2+bx-c=0, then the equation whose roots are b and c is
- The roots of the quadratic equation (a+b-2c)x^2-(2a-b-c)x+(a-2b+c)=0 are
- The product of the real roots of the equation |2x+3|^2-3|2x+3|+2=0, is
- If one root of the equation x^2+px+12=0 is 4, while the equation x^2+px+q=0 has equal roots, then the value of q is
- The number of real roots of the equation 2x^4+5x^2+3=0, is
- The roots of the equation (3-x)^4+(2-x)^4=(5-2x)^4 are