Question

Assertion (A): The roots of the quadratic equation 8x² + 2x – 3 = 0 are `-1/2` and `3/4`.

Reason (R): The roots of the quadratic equation ax² + bx + c = 0 are given by `x = (-b ± sqrt(b^2 - 4ac))/(2a)`

पर्याय

• A is true, R is false

• A is false, R is true

• Both A and R are true

• Both A and R are false

Answer 1

A is false, R is true

Explanation:

Use the quadratic formula from R:

`x = (-b ± sqrt(b^2 - 4ac))/(2a)`

This formula is correct.

For 8x² + 2x – 3 = 0: a = 8, b = 2, c = –3. 

Discriminant D = 2² – 4 × 8 × (–3) 

= 4 + 96

= 100

`sqrt(D) = 10`

So, `x = (-2 ± 10)/16`

`x = 8/16`

`x = 1/2` 

or

`x = -12/16`

`x = -3/4`

Assertion is wrong it stated `-1/2` and `3/4`, which are the signs swapped, so A is false while R is true.