If 2 is a root of the equation x² + bx + 12 = 0 and the equation x² + bx + q = 0 has equal roots, then q =
(a)8
(b)−8
(c)16
(d)−16
Answers
SOLUTION :
Option (c) is correct : 16
Given : 2 is the root of x² + bx + 12 = 0 ………..(1)
and x² + bx + q = 0 has equal roots………(2)
Since, x = 2 is a root of equation (1) so it will satisfy the equation.
On putting x = 2 in equation (1)
x² + bx + 12 = 0
(2)² + 2b + 12 = 0
4 + 2b + 12 = 0
16 + 2b = 0
2b = - 16
b = -16/2
b = - 8
On putting b = - 8 in equation (2)
x² + bx + q = 0
x² + (- 8)x + q = 0
x² - 8x + q = 0
On comparing the given equation with ax² + bx + c = 0
Here, a = 1 , b = - 8 , c =
D(discriminant) = b² – 4ac
D = (- 8)² - 4(1)(q)
D = 64 - 4q
D = 0 ( Equal roots given)
64 - 4q = 0
64 = 4q
q = 64/4
q = 16
Hence the value of q is 16 .
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Ans is 16 because 2 is the root equation then 4+2k+12 =0 so
2k+16=0
2k= -16
K=-8
X2+kx+q=0
x2-8k+q=0
So b2=4ac
64=4*1*q
Q= 16