Q20 of 40 Page 1

Find the value(s) of k for which the quadratic equation x2 + 2√2 kx + 18 = 0 has equal roots.


Given - Equation x2 + 2√2 kx + 18 = 0 has equal roots


To Find – value of k


Properties –


The condition for the equation ax2 + bx + c = 0 to have equal roots is b2 = 4ac


Answer –


Comparing given equation with ax2 + bx + c = 0, we get,


a = 1, b = 2√2 k and c = 18


As given equation has equal roots.


∴ b2 = 4ac


∴ (2√2 k)2 = 4 × 1 × 18


∴ 8k2 = 4 × 18


∴ 8k2 = 72


∴ k2 = 9


∴ k = ±3


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