Question

determine whether the given quadratic equation has real roots if so find the roots 2 x square minus 2 root 2 X + 1 equal to zero​

Answer 1

❌$\huge\mathbb\red{ANSWER}$❌

if roots are real then D = 0

$as \: we \: know \: \\ \\ \huge \color{brown}{d= {b}^{2} - 4ac}$

so

${b}^{2} - 4ac \: = 0$

where a = 2 b = -2√2 c =

1

then

$( { - 2 \sqrt{2}) }^{2} - 4(2)(1) = 0 \\ \\ 8 -8 = 0 \\ \\ 0 = 0 \\ \\ hence \: proved \:$

Now we have to find root

2x² - 2√2x + 1

by using quadratic formula

$\huge \color{indigo}{x = \frac{ - b ± \sqrt{ {b}^{2} - 4ac } }{2a} }$

by putting value

$x = \frac{ - (- 2\sqrt{2}) ± \sqrt{ { (- 2 \sqrt{2}) }^{2} } - 4(2)(1) }{2(2)} \\ \\ x = \frac{2 \sqrt{2 } ± \sqrt{8 - 8} }{4} \\ \\ x = \frac{2 \sqrt{2} ± \sqrt{0} }{4} \\ \\ x = \frac{ 2\sqrt{2} }{4} \\ \\ x = \frac{ \sqrt{2} }{2}$

hope it helps you

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