QQuestion
If the sum of the square of the roots of the equation 6x² + x + k = 0 is 25\over36, then the value of k is 12.
✓Answer
False
Explanation:
The sum of the squares of the roots of a quadratic equation ax^2 + bx + c = 0 is given by:
α2 + β2 = (α + β)2 – 2αβ
From the given equation 6x² + x + k = 0,
Sum of roots: α + β = -\frac{b}{a} = -\frac{1}{6}
Product of roots: α × β = \frac{c}{a} = \frac{k}{6}
Using the formula:
\left(-\frac{1}{6} \right)^2 - 2 \times \frac{k}{6} = \frac{25}{36}
Solving, k \neq 12
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