Question

If one zero of the quadratic polynomial 2 x square - 8 x minus m is 5/2. find m and the value of other zero..

Answer 1

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Given ,

The quadratic equation is 2x² - 8x - m = 0 and x = 5/2

We have to find the value of m , So , substitute the value of x = 5/2 in given quadratic equation , we obtain

$\sf \hookrightarrow 2 {( \frac{5}{12} )}^{2} - 8 ( \frac{5}{12} ) - m = 0 \\ \\ \sf \hookrightarrow 2( \frac{25}{144} ) - (\frac{40}{12} ) - m = 0 \\ \\ \sf \hookrightarrow \frac{50}{144} - \frac{40}{12} - m = 0 \\ \\ \sf \hookrightarrow \frac{50 - 40(12) - m(144)}{144} = 0 \\ \\ \sf \hookrightarrow 50 -48 0 - 144m = 0 \\ \\ \sf \hookrightarrow - 420 - 144m = 0 \\ \\ \sf \hookrightarrow m = - \frac{420}{144} \\ \\ \sf \hookrightarrow m = - \frac{35}{12}$

Hence , the value of m is -35/12