Find the values of k for which the equation has real roots . (k-12x^2+ 2(k-12) x+2=0 Write the answer fast then I will mark you brainliest .
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The given quadratic will be a perfect square if it has two real and equal roots. To have two real and equal roots the discriminant must be zero.
i.e., b²-4ac=0
or, (2k+4)²-4(4-k)(8k+1)=0
or, 4k²+16k+16-4(32k-8k²+4-k)=0
or, 4k²+16k+16-128k+32k²-16+4k=0
or, 36k²-108k=0
or, 36k(k-3)=0
either 36k=0
or, k=0
or, k-3=0
or, k=3
∴, k=0,3
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