Question

In the questions two columns are given. You are required to solve the equations given in the "equations" column and match them with the correct statement given about the desired equation in the "conditions" column.

	Equations		Conditions
(a)	2x2 – 11x + 12 = 0	(d)	Product of roots is negative
(b)	5x2 21x – 20 = 0	(e)	Product of roots is completely divisible by 6
( c)	x2 – 17x + 72 = 0	(f)	Sum of both roots is positive

• A. (a) – (e) and (f), (b) – (d), (c) – (e)
• B. (a) – (e) and (f), (b) – (d) and (f) and (c) – (e) and (f)
• C. (a) – (e) and (f), (b) – (d) and (f) and (c) - (d) and (f)
• D. (a) – (f), (b) – (d) and (e), (c) – (e) and (f)
• E. None of these

Answer 1

The Correct Option is C

For (a):
2x2 - 11x + 12 = 0
Or, 2x2 - 8x - 3x + 12 = 0
Or, 2x(x – 4) – 3(x – 4) = 0
Or, (2x - 3)(x – 4) = 0
Or, x = \(\frac{3}{2}\) or x = 4
Sum of roots = (\(\frac{3}{2}\)) + 4 = 11/2 (positive)
Product of roots = (\(\frac{3}{2}\)) * 4 = 6 (positive)
Since, \(\frac{6}{6}\)= 1
So, larger root is completely divisible by '6'.
So, equation (a) satisfies the condition given in (e) as well as (f).
For (b):
5x² - 21x - 20 = 0
Or, 5x² - 25x + 4x - 20 = 0
Or, 5x(x - 5) + 4(x - 5) = 0
Or, (5x + 4)(x - 5) = 0
Or, x = -\(\frac{4}{5}\) or x = 5
Sum of roots = (-\(\frac{4}{5}\)) + 5 = \(\frac{21}{5}\) (positive)
Product of roots = -\(\frac{4}{5}\) × 5 = -4 (negative)
Since, \(\frac{21}{5}\) is not completely divisible by '6'.
So, equation (b) satisfies the condition given in (d) and (f).
For (c):
x² - 17x + 72 = 0
Or, x² - 8x - 9x + 72 = 0
Or, x(x - 8) - 9(x - 8) = 0
Or, (x - 9)(x - 8) = 0
Or, x = 9 or x = 8
Sum of roots = 9+ 8 = 17 (positive)
Product of roots = 9 × 8 = 72 (positive)
Since, 72 is completely divisible by 72 i.e. \(\frac{72}{6}\) = 12
So, equation (c) satisfies the condition given in (e) and (f).