Find whether the equation 8x² + 2x – 3 = 0 has real roots. If real roots exist, find them.

Given: equation 8x² + 2x – 3 = 0.

To find: The roots if the equation has real roots.

Formula Used:

If a quadratic equation

ax² + bx + c = 0, a ≠ 0 has two equal roots, then its discriminant value will be equal to zero i.e.,

D = b² - 4ac > 0

Explanation:

To check whether the quadratic equation has real roots or not, we need to check the discriminant value i.e.,

D = b² - 4ac

For 8x² + 2x – 3 = 0

⸫ D = 2² - 4(8) (-3)

⇒D = 4 + 96 > 0

Hence, the roots are real and distinct.

To find the roots, use the formula,

Hence the roots are .