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The roots of $ax^2+bx+c=0$ are $r$ and $s$. For the roots of $x^2+px+q=0$ to be $r^2$ and $s^2$, what must be the value of $p$ ?

(A) $\large\frac{b^2-4ac}{a^2}$
(B) $\large\frac{b^2-2ac}{a^2}$
(C) $\large\frac{2ac-b^2}{a^2}$
(D) $b^2-2c$

1 Answer

  • Sum of the roots of $ax^2+bx+c=0$ is $\large-\frac{b}{a}$
  • Product of the roots = $\large\frac{c}{a}$
  • $a^2+b^2=(a+b)^2-2ab$
  • Quadratic equation whose roots are $\alpha\:\:and\:\:\beta$ is $x^2-(\alpha+\beta)x+\alpha\beta$
Given: $r\:\:and\:\:s$ are roots of $ax^2+bx+c=o$
$\Rightarrow\:r+s=\large-\frac{b}{a}$ and $rs=\large\frac{c}{a}$
Quadratic Eqn., whose roots are $r^2\:\:and\:\:s^2$ is
Given: $x^2+px+q=0$ is equation whose roots are $r^2\:and\:s^2$
answered Jul 17, 2013 by rvidyagovindarajan_1

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