Find a quadratic equation whose product of roots `x_1a n dx_2` is equal to 4 an satisfying the relation `(x_1)/(x_1-1)+(x_2)/(x_2-1) =2.`

Find a quadratic equation whose roots x_(1) and x_(2) satisfy the condition x_(1)^(2)+x_(2)^(2)=5,3(x_(1)^(5)+x_(2)^(5))=11(x_(1)^(3)+x_(2)^(3)) (assume that x_(1),x_(2) are real)

If a>1 is a constant satisfying the relation int_(1)^(a)(x-1)/(x+sqrt(x))dx=4. The value of a^(2)+a+1

The quadratic equation whose roots are the arithmetic mean and the harmonic mean of the roots of the equation x^(2)+7x-1=0 is

Find k so that the quadratic equation (k + 1)x^(2) - 2(k + 1)x + 1 = 0 has equal roots.

The roots of the equation (x+2)^(2)=4(x+1)-1 are

Find m, if the quadratic equation (m-1)x^2-2(m-1)x+1=0 has real and equal roots.