Telangana Board Solutions for Exercise 2: Exercise 4(b)

Solve the following equations, given that they have multiple roots.$3x^4+16x^3+24x^2-16=0$.

Solve $x^4+x^3-16x^2-4x+48=0$, given that the product of two of the roots is $6$.

Solve $8x^4-2x^3-27x^2+6x+9=0$ given that two roots have the same absolute value, but are opposite in sign.

Solve $18x^3+81x^2+121x+60=0$ given that one root is equal to half the sum of the remaining roots.

Find the condition in order that the equation $a{x}^4+4b{x}^3+6c{x}^2+4dx+e=0$ may have two pairs of equal roots.

Show that $x^5-5x^3+5x^2-1=0$ has three equal roots and find this root.

Find the repeated roots of $x^5-3x^4-5x^3+27x^2-32x+12=0$.

Solve the equation $8x^3-20x^2+6x+9=0$ given that the equation has multiple roots.