Question

find whether the quadratic equations 8x2 + 2x -3 =0 have real roots. if real roots exists, find them​

Answer 1

Solution:-

Equation:-

$\rm \: 8 {x}^{2} + 2x - 3 = 0$

Compare with

$\rm \: a {x}^{2} + bx + c = 0$

We get

$\rm \: a = 8 \: \: \: \: b = 2 \: \: \: and \: \: \: c \: = - 3$

Find Discriminant

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

$\rm \: D = (2) {}^{2} - 4 \times 8 \times - 3$

$\rm \: D = 4 + 96$

$\rm \: D = 100$

D > 0 so, Nature of root is Real , Distinct

So using quadratic formula

$\boxed{ \bf \: x = \frac{ - b \pm \sqrt{D} }{2a} }$

put the value on quadratic formula

$\rm \: x = \frac{ - 2 \pm \: \sqrt{100} }{2 \times 8}$

$\rm \: x = \frac{ - 2 \pm10}{16}$

$\rm \: x = \frac{ - 2 + 10}{16} \: \: and \: \: \frac{ - 2 - 10}{16}$

$\rm \: x = \frac{8}{16} \: \: and \: \: \frac{ - 12}{16}$

Answer

$\rm \: x = \frac{1}{2} \: \: and \: \: \frac{ - 3}{4}$