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Question
Find the value(s) of k so that the quadratic equation 3x2 − 2kx + 12 = 0 has equal roots ?
Solution
The given quadratic equation is 3x2 − 2kx + 12 = 0
On comparing it with the general quadratic equation ax2 + b x + c = 0, we obtain
a = 3, b = −2k and c = 12
Discriminant, ‘D’ of the given quadratic equation is given by
D = b2 − 4ac
= (− 2k)2 − 4 × 3 × 12
= 4k2 − 144
For equal roots of the given quadratic equations, Discriminant will be equal to 0.
i.e., D = 0
`rArr 4k^2-144=0`
`rArr4(k^2-36)=0`
`rArrk^2=36`
`rArrk=+-6`
Thus, the values of k for which the quadratic equation 3x2 − 2kx + 12 = 0 will have equal roots are 6 and −6.
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