Question

If 2 is a root of the equation x^2 + bx + 12 = 0 and the equation x^2 + bx + q = 0 has equal roots, then q is equal to

Answer 1

Answer:

Put x=2

2*2+b*2+12=0

16+2b=0

Hence,b=-8

Now put x=2and b=-8in other equation

2*2+-8*2+q=0

4-16+q=0

-12+q=0

So q=12

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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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