Quadratic EquationHard

Question

Let ' p ' is a root of the equation $x^{2} - x - 3 = 0$. Then the value of $\frac{p^{3} + 1}{p^{5} - p^{4} - p^{3} + p^{2}}$ is equal to

Options

A.$\frac{4}{3}$
B.$\frac{4}{9}$
C.$\frac{2}{9}$
D.$\frac{2}{3}$

Solution

$\frac{p^{3} + 1}{\left( p^{4} - p^{2} \right)(p - 1)} = \frac{(p + 1)\left( p^{2} - p + 1 \right)}{p^{2}(p - 1)^{2}(p + 1)} = \frac{p^{2} - p + 1}{\left( p^{2} - p \right)^{2}} = \frac{3 + 1}{(3)^{2}} = \frac{4}{9}$

Create a free account to view solution

View Solution Free
Topic: Quadratic Equation·Practice all Quadratic Equation questions

More Quadratic Equation Questions

If all the roots of the equation $x^{4} - 12x^{3} + ax^{2} + bx + 81 = 0$ where $a,b \in R$ are positive, then...If α and β are roots of 2x2 − 7x + 6 = 0, then the quadratic equation whose roots are is-...If x be real then the value of will not lie between -...The degree of the polynomial $p(x)$ which satisfies the condition $(x)p(x - 1) = (x - 15)p(x)$ is :...If the equation ax2 + 2bx − 3c = 0 has no real roots and < a + b, then-...