Question

The equation x² - 2x - 8 = 0 will have
1. the numerically larger root as negative.
2. the numerically larger root as positive.
3. both roots as negative.
4. both roots as positive.

Answer 1

Correct Answer - Option 2 : the numerically larger root as positive.

Calculation:

Given the equation, x2 - 2x - 8 =0      ...(1)

As we know, the sum of roots = \(-b\over a\) and, the product of roots = \(c\over a\)

From equation (1), the sum of roots = -(-2)/1 = 2

and, the product of roots = -8

Since the product of the roots is negative ⇒ one of the roots is positive and the other is negative.

Since the sum of the roots is positive ⇒ the positive root is numerically larger than the negative root.

So, The equation x2 - 2x - 8 =0 will have the numerically larger root as positive.

For a quadratic equation of the form, ax² + bx + c = 0, we can use the following table to determine the sign of the roots of the equation. 

Sign of the product of the roots	Sign of the sum of the roots	Sign of the roots
+ ve	+ ve	Both the roots are positive.
+ ve	- ve	Both the roots are negative.
- ve	+ ve	The numerically larger root is positive and the other root is negative.
- ve	-ve	The numerically larger root is negative and the other root is positive.