Question

b^2-10b+32=o, then b=? ​

Answer 1

Step-by-step explanation:

$\huge\underline{\underline{\ Question}}$

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${b}^{2} - 10b + 32 = 0$

Solve and find the value of b.

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$\huge\underline{\underline{\ Answer}}$

${b}^{2} - 10b + 32 = 0 \\ comparing \: with \\ \boxed{a {x}^{2} + bx + c = 0} \\ a = 1 \\ b = - 10 \\ c = 32$

Now, By using quadratic formula..

$\implies b = \frac{ - b + \: or \: - \sqrt{ {b}^{2} - 4ac } }{2a} \\ \implies b = \frac{10 + \: or \: - \sqrt{100 - 128} }{2} \\ \implies b = \frac{10 + \: or \: - \sqrt{ - 28} }{2}$

Here, we got negative number under square root

So the roots are not real but you can solve it futher by using complex numbers....

$\implies b = \frac{10 + \: or \: - \sqrt{28} \times \sqrt{ - 1} }{2} \\ \implies b = \frac{10 + \: or \: - \sqrt{ 4 \times 7} \: \: i }{2} \\ \implies b = \frac{10 + \: or \: - 2 \sqrt{7} \: \: \: i }{2} \\ \implies b = \frac{ \cancel2(5 + \: or \: - \sqrt{7} \: i)}{ \cancel2} \\ \implies b = 5 + \: or \: - \sqrt{7} \: i \\ \implies \huge \boxed{b = 5 + \sqrt{7} \: \: i \: \: or \: \: b = 5 - \sqrt{7} \: i}$