Determine if the equation has real roots and if so, find the roots. (CBSE 2017)

Given: The equation ,

To find: The roots if real.

Formula Used:

For a quadratic equation, ax² + bx + c = 0,

D = b² – 4ac

If D < 0, roots are not real

If D > 0, roots are real and unequal

If D = 0, roots are real and equal

The quadratic formula for finding the roots of quadratic equation
ax² + bx + c = 0, a ≠ 0 is given by,

Explanation:

Consider,

Here a= √2, b = 7, c = 5√2

⇒ D = b² – 4ac

⇒ D = 49 – (4 × 5√2 × √2)

= 49 – (20 × 2)

= 49 - 40

= 9 > 0

By quadratic formula,

Hence the roots are .