AP EAMCET202017 Sep 2020Evening ShiftMathematicsQuadratic EquationActual

Equation (x^5-5 x^3+5 x^2-1=0 ) has equal roots

Options

Correct answer

B. 3

Step-by-step solution

Given, (f(x)=x^5-5 x^3-5 x-1=0 ) Now by inspection, (x=1 is a zero of f(x) ) So, we can divide (f(x) ) by (x-1 ) to get, (f(x)=(x-1) (x^4+x^3-4 x^2+x+1 ) ) We similarly proceed to get ( aligned & f(x)=(x-1)(x-1) (x^3+2 x^2-2 x-1 ) & f(x)=(x-1)(x-1)(x-1) (x^2+3 x+1 ) aligned ) So, (f(x) ) has 3 equal roots.

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