Question

Find the nature of roots of the quadratic equation 2x^2 - 4x - 3 = 0 . If real roots exist, find them.​

Answer 1

Answer :-

To find the nature of roots, we first need to find discrimination (D) -

$\sf D = b^2 - 4ac$

$\sf D = -4^2 - 4 ( -3)(2)$

$\sf D = 16 + 24$

$\sf D = 40$

Here, D > 0 so the roots of this quadratic equation are real and distinct.

By using quadratic formula :-

$\boxed{\rm x = \dfrac{-b \pm \sqrt{b^2 - 4ac} }{2a}}$

• a = 2
• b = - 4
• c = - 3

Substituting the value in formula :-

$\sf x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4(2)(-3)} }{2 \times 2}$

$\sf x = \dfrac{4 \pm \sqrt{16 + 24} }{4}$

$\sf x = \dfrac{4 \pm \sqrt{40} }{4}$

$\sf x = \dfrac{ 4 \pm 2\sqrt{10} }{4}$

$\boxed{\sf x = 1 + \dfrac{ \sqrt{10} }{2} \: , 1\: - \dfrac{ \sqrt{10} }{2}}$