Question

Find the nature of the roots of the quadractic equation 5xsquare -5x +7=0

Answer 1

Question :-

Find the nature of the roots of the quadractic equation 5x² - 5x + 7 = 0 .

Answer :-

$\to \: </p><p>D < 0 \: \\ \sf roots \: are \: imaginary \: \:$

To Find :-

→ Nature of roots .

Solution :-

if we have a quadratic → ax² + bx + c = 0 ,

For Identify the nature of roots we have to find discriminant of that quadratic equation .

which is -

→ D = b² - 4ac

If -

• D = 0 ( real and equal roots )

• D > 0 ( real and distinct roots )

• D < 0 ( imaginary roots )

So ,we have quadratic equation -

$\to \rm 5 {x}^{2} - 5x + 7 = 0 \\ \: \bf \: here \: \\ \rm \: a = 5 , b = -5 \: and \: c = 7 \: \\ \\ \bf \: so \: \\ \rm</p><p>→ D = {b}^{2} - 4ac \: \\ \\ \: </p><p> \: \: \: \: \: \: \: \: = {( - 5)}^{2} - 4 \times 5 \times 7 \: \\ \\ \: \: \: \: \: \: \: \: \: = 25 - 140 \\ \\ \: \: \: \: \: \: \: \: \: = - 115 \\ \\ \sf here \\ \to \: </p><p>D < 0 \: \\ \sf roots \: are \: imaginary \: \\ \\ \sf for \: finding \: imaginary \: roots \\ \sf we \:will \: use \: shree \: dharacharya \: formula \\ \\ \boxed{\rm \to \: x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }$