SSC CGL 9 Aug 2017 Shift 1 Paper

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Question : 61 of 100

Marks: +1, -0

If (x - 2 ) and (x + 3) are the factors of the equation

x^ 2 +k_1x + k_2 = 0

, then what are the values of

k_1

and

k_2

?

$k_1=6, k_2 = 1$
$k_1=1, k_2 = -6$
$k_1=1, k_2 =6$
$k_1=-6, k_2 = 1$

Solution:

x^ 2 +k_1x + k_2 = 0

x - 2 = 0
Putting x = 2,
⇒

4 + 2 k_1 + k_2 = 0

⇒

2k_1+k_2=-4

..... (i)
∴

x + 3 =0

Putting x = - 3,
⇒

9 - 3 k_1 + k_2 = 0

⇒

3k_1 - k_2 = 9

......(ii)
On solving Eqs. (i) and (ii),

k_1= 1,k _2 = -6

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