Question

x^2+px-q^2=0 show roots of equation are real for all values of p and q​

Answer 1

eqn. is

${x}^{2} + px - {q}^{2} = 0 \\ here \\ d = {p}^{2} - 4(1)( - {q}^{2} ) = {p}^{2} + 4 {q}^{2} > = 0 \\ hence \: for \: all \: values \: of \: p \: and \: q \\ both \: the \: roots \: of \: the \: above \: eq. \: \\ are \: real.$