Question

5m2 +5m =1 quradratic educations​

Answer 1

$\sf \: {5m}^{2} + 5m = 1$

Write it in general form.

$\sf \: {5m}^{2} + 5m - 1 = 0$

Comparing with am² +bm + c= 0 ,

$\sf a = 5, \: b = 5 \: , \: c = - 1$

$\sf \therefore \: {b}^{2} - 4ac = (5)^{2} - 4 \times 5 \times - 1$

$\sf \: = 25 - 20 \times - 1$

$\sf \: = 25 + 20$

$\green{ \sf \: \therefore \: {b}^{2} - 4ac = 45}$

Now , By Using Quadratic formula,

$\sf \: m = \dfrac{ - b \pm \: \sqrt{ {b}^{2} - 4ac } }{2a}$

$\sf \:m = \dfrac{ - 5 \pm \: \sqrt{45} }{2 \times 5}$

$\sf \: m = \dfrac{ - 5 \pm \: \sqrt{45} }{10}$

$\sf m = \dfrac{ - 5 \pm \: \sqrt{9 \times 5} }{10}$

$\sf \: m = \dfrac{ - 5 \pm \: 3\sqrt{5} }{10}$

$\sf\: m = \dfrac{ - 5 + 3 \sqrt{5} }{10} \: \: \: or \: \\ \sf m = \dfrac{ - 5 - 3 \sqrt{5} }{10}$