The solution set of the equation $pq{x^2} - {(p + q)^2}x + {(p + q)^2} = 0$ is
$\left\{ {\frac{p}{q},\,\frac{q}{p}} \right\}$
$\left\{ {pq,\,\frac{p}{q}} \right\}$
$\left\{ {\frac{q}{p},\,pq} \right\}$
$\left\{ {\frac{{p + q}}{p},\,\frac{{p + q}}{q}} \right\}$
For what value of $\lambda$ the sum of the squares of the roots of ${x^2} + (2 + \lambda )\,x - \frac{1}{2}(1 + \lambda ) = 0$ is minimum
One root of the following given equation $2{x^5} - 14{x^4} + 31{x^3} - 64{x^2} + 19x + 130 = 0$ is
The number of cubic polynomials $P(x)$ satisfying $P(1)=2, P(2)=4, P(3)=6, P(4)=8$ is
Let $p, q$ be integers and let $\alpha, \beta$ be the roots of the equation, $x^2-x-1=0$, where $\alpha \neq \beta$. For $n=0,1,2, \ldots$, let $a_n=$ $p \alpha^n+q \beta^n$.
$FACT$ : If $a$ and $b$ are rational numbers and $a+b \sqrt{5}=0$, then $a=0=b$.
($1$) $a_{12}=$
$[A]$ $a_{11}-a_{10}$ $[B]$ $a_{11}+a_{10}$ $[C]$ $2 a_{11}+a_{10}$ $[D]$ $a_{11}+2 a_{10}$
($2$) If $a_4=28$, then $p+2 q=$
$[A] 21$ $[B] 14$ $[C] 7$ $[D] 12$
answer the quetion ($1$) and ($2$)
Equation $\frac{3}{{x - {a^3}}} + \frac{5}{{x - {a^5}}} + \frac{7}{{x - {a^7}}} = 0,a > 1$ has