Question

if 2 is the root of the equation x^2 +bx+12=0 & the equation x^2+bx+q=0 has equal roots then q=??

Answer 1

x²+bx+12 = 0
or, 4+2b+12 = 0 [ the root is 2]
or, b = -8

x² +bx+q = 0
or, x²-8x+q = 0

Now,
b²-4ac = 0 [the roots are equal]
or, (-8)²-4×1×q = 0
or, q=16

Answer 2

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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