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प्रश्न
If 2 is a root of the equation x2 + ax + 12 = 0 and the quadratic equation x2 + ax + q = 0 has equal roots, then q =
पर्याय
12
8
20
16
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उत्तर
x = 2is the common roots given quadric equation are `x^2 + ax + 12 = 0`, and `x^2 + ax + q = 0`
Then find the value of q.
Here, `x^2 + ax + 12 = 0` ….. (1)
`x^2 + ax + q = 0` ….. (2)
Putting the value of x = 2 in equation (1) we get
`2^2 + a xx 2 + 12 = 0`
4 + 2a + 12 =0
2a =-16
a = -8
Now, putting the value of a = - 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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