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प्रश्न
If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q =
विकल्प
8
-8
16
-16
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उत्तर
2 is the common roots given quadric equation are x2 + bx + 12 = 0 and x2 + bx + q = 0
Then find the value of q.
Here, x2 + bx + 12 = 0 ….. (1)
x2 + bx + q = 0 ….. (2)
Putting the value of x = 2 in equation (1) we get
`2^2 + b xx 2 + 12 = 0`
`4 + 2b + 12 = 0`
`2b = - 16`
`b = -8`
Now, putting the value of b = -8 in equation (2) we get
`x^2 -8x + q = 0`
Then,
`a_2 = 1,b_2 = -8 and , c_2 = q`
As we know that `D_1 = b^2 - 4ac`
Putting the value of `a_2 = 1,b_2 = -8 and , c_2 = q`
`= (-8)^2 - 4 xx 1 xx q`
`= 64 - 4q`
The given equation will have equal roots, if D = 0
`64 - 4q = 0`
`4q = 64`
`q = 64/4`
`q = 16`
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