Question

$8x { }^{2} - 22x - 21 = 0 \: by \: using \: quadratic \: formula$
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Answer 1

     

p(x) = 8x² - 22x - 21 = 0

a = 8

b = -22

c = -21

⇒ b² - 4ac

⇒ (-22)² - (4 · 8 · -21)

⇒ 484 - (-672)

⇒ 484 + 672

⇒ 1156

$\leadsto\ \boxed{\bold{x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}}} \\ \\ \leadsto\ \boxed{\bold{x=\frac{22\pm\sqrt{1156}}{16}}} \\ \\ \leadsto\ \boxed{\bold{x=\frac{22\pm34}{16}}} \\ \\ \leadsto\ \boxed{\bold{x=\textit{3.5}}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \boxed{OR}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \boxed{\bold{x=\textit{-0.75}}}$

So the roots of p(x) are 3.5 and -0.75!!!

     

Thank you...

$\mathfrak{\#adithyasajeevan}$

   

Answer 2

$(i) \: Solution : \: \: \: \: \: We, \: have \: 8x {}^{2} - 22x - 21 = 0 \\ ⇒8x {}^{2} - 28x + 6x - 21 = 0 \\ ⇒4x(2x - 7) + 3(2x - 7) = 0 \\ ⇒(2x - 7)(4x + 3) = 0 \\ ⇒2x - 7 = 0 \: or \: 4x + 3 = 0 \\ ⇒x = \frac{7}{2} \: or \: x = \frac{ - 3}{4} \\ Thus, \: x = \frac{7}{2} \: and \: x = \: \frac{ - 3}{4} are \: two \: roots \: of \: given \: equation.$