Question

write all the values of p for which the quadratic equatioln X square + PX + 16 equal to zero has equal roots find the roots of equations obtain​

Answer 1

i it may help.........

Answer 2

$\: \: \: \: \: \: \: \: \: \: \: \: {x}^{2} + px + 16 = 0$

$as \: the \: equation \: have \: equal \: roots\\so \: \: \: \: \red{\boxed { b {}^{2} - 4ac = 0}}$

$here \: \: \: \: a = 1 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: b = p \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: c = 16$

$\: \: \: \: \: \: \: \: \: \: \: \: {p}^{2} - 4(1)(16) = 0$

$\: :⟹ \: \: \: \: \: \: \: \: \: \: {p}^{2} - 64 = 0$

$\: \: :⟹ \: \: \: \: \: \: \: \: \: \: \: {p}^{2} = 64$

$\: \: \: \: :⟹ \: \: \: \: \: \: \: \: \: p = \sqrt{64}$

$\: \: \: : ⟹ \: \: \: \: \: \: \: \: \: \ \fcolorbox{blue}{pink}{\fcolorbox{green}{aqua} {p = ±8}}$

$\: \: \: \: \: \: \: \: \: p(x) = {x}^{2} + px + 16$

$when \: \: \: \: \pink{p = 8}$

$:⟹ \: \: \: {x}^{2} + 8x + 16 = 0$

$: ⟹ \: \: {x}^{2} + 4x + 4x + 16 = 0$

$: ⟹x(x + 4) + 4(x + 4) = 0$

$: ⟹ \: \: \: \: (x + 4)(x + 4) = 0$

$: ⟹ \: \: \: \: \: \: \: \: \: \: \: \boxed{x = - 4}$

$when \: \: \: \pink{p = - 8}$

$: ⟹ {x}^{2} - 8x + 16 = 0$

$: ⟹ {x}^{2} - 4x - 4x + 16 = 0$

$: ⟹x(x - 4) - 4(x - 4) = 0$

$: ⟹(x - 4)(x - 4) = 0$

$: ⟹ \: \: \: \: \: \: \: \: \boxed{x = 4}$

$\underbrace\mathcal\red{Please\:mark\:as\:\:Brainliest..............}$