(i) Given that x+ 2kx + 4k - 3 = 0 has no real roots, show that k satisfies k- 4k + 3 <0. (ii) Solve the inequality k - 4k + 3 < 0.

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A: We have to solve the rational inequality  x2-3x-4x2+6x+9 ≤ 0.

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A: this inequality is positive if all are positive or if two is negative and other is positive

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A: The given inequality (x - 4)(x + 2) &gt; 0 .

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A: in the given question we have to solve the inequalities and express the solution as intervals .we…

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A: Topic = Inequality

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A: The solution is given below in the next step:

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A: We set each factor equal to 0.

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A: The given inequality is: 4x-3&lt;0.01 Now use the modulus definition : If x&lt;a than -a&lt;x&lt;a

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