Question

The roots of a quadratic equation x2 - 4px
+ 4p2 - q2 = 0 are​

Answer 1

$\textbf{Given:}$

$x^2-4p\,x+(4p^2-q^2)=0$

$\textbf{To find:}$

$\text{The roots of the given quadratic equation}$

$\textbf{Solution:}$

$\text{Consider,}$

$x^2-4p\,x+(4p^2-q^2)=0$

$\text{Here,}\;a=1,\;b=-2p,\;c=4p^2-q^2$

$\text{Then, the roots are}$

$\bf\,x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\dfrac{4p\pm\sqrt{(-4p)^2-4{\times}1{\times}4p^2-q^2}}{2(1)}$

$x=\dfrac{4p\pm\sqrt{16p^2-16p^2+4q^2}}{2}$

$x=\dfrac{4p\pm\sqrt{4q^2}}{2}$

$x=\dfrac{4p\pm\,2q}{2}$

$x=2p\pm\,q$

$\textbf{Answer:}$

$\textbf{The roots are}$

$\bf\,2p+q\;\&\;2p-q$

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