Let $\alpha$ and $\beta$ be the roots of the equation $\mathrm{x}^{2}-\mathrm{x}-1=0 .$ If $\mathrm{p}_{\mathrm{k}}=(\alpha)^{\mathrm{k}}+(\beta)^{\mathrm{k}}, \mathrm{k} \geq 1,$ then which one of the following statements is not true?
$\left(p_{1}+p_{2}+p_{3}+p_{4}+p_{5}\right)=26$
$\mathrm{p}_{5}=11$
$\mathrm{p}_{3}=\mathrm{p}_{5}-\mathrm{p}_{4}$
$\mathrm{p}_{5}=\mathrm{p}_{2} \cdot \mathrm{p}_{3}$
If $a < 0$ then the inequality $a{x^2} - 2x + 4 > 0$ has the solution represented by
The number of real roots of the polynomial equation $x^4-x^2+2 x-1=0$ is
Suppose $m, n$ are positive integers such that $6^m+2^{m+n} \cdot 3^w+2^n=332$. The value of the expression $m^2+m n+n^2$ is
If the graph of $y = ax^3 + bx^2 + cx + d$ is symmetric about the line $x = k$ then
The number of the real roots of the equation $(x+1)^{2}+|x-5|=\frac{27}{4}$ is ....... .