Question

$\sf \: The\:roots\:of\:the\: quadratic\: equation \: 4 {x}^{2} \: - 7x + 2 = 0 \: are \: 1.390 \: and \: 0.359 . \\ \: \sf \: The \: roots \: correct \: to \: 2 \: significant \: figures \: are \:$
$\sf \: @\:The\:Brain\: don't\:delete\:my\:questions \: it \: isn't \: violating \: brainly \: guidlines$
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Answer 1

Answer:

$\displaystyle \: x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 4\times 2}}{2\times 4}$

$\displaystyle \: x=\frac{-\left(-7\right)±\sqrt{49-4\times 4\times 2}}{2\times 4}$

$\displaystyle \: x=\frac{-\left(-7\right)±\sqrt{49-32}}{2\times 4}$

$\displaystyle \: x=\frac{-\left(-7\right)±\sqrt{17}}{2\times 4}$

$\displaystyle \: x=\frac{7±\sqrt{17}}{2\times 4}$

$\displaystyle \: x=\frac{7±\sqrt{17}}{8}$

$\displaystyle \: x = \frac{7 - \sqrt{17} }{8} \: or \: x = \frac{ \sqrt{17} + 7}{8}$

$x=\frac{\sqrt{17}+7}{8} = 1. 390\\ x=\frac{7-\sqrt{17}}{8} = 0.359$

Hence, The approximate value is correct.