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# Which of the intervals contains the roots of the f(x) = x^{2} - 7x + 12?

(3, 4), (4, 5), [2, 6] and [3, 4]

**Solution:**

Quadratic equations are equations having degree equal to two; it has many applications in various fields other than mathematics.

To solve the given equation we use the method of splitting the middle term.

Given equation: f(x) = x^{2} - 7x + 12

⇒ f(x) = x^{2} - 7x + 12

⇒ f(x) = x^{2} - 4x - 3x + 12

⇒ f(x) = x(x - 4) - 3(x - 4)

⇒ f(x) = (x - 3)(x - 4)

Now to find the root, we equate f(x) to zero.

Hence, (x - 3)(x - 4) = 0

⇒ x - 3 = 0 or x - 4 = 0

⇒ x = 4 or x = 3

Hence, among the given options, the roots of the equation f(x) = x^{2} - 7x + 12 lies in the intervals [2, 6] and [3, 4] both.

## Which of the intervals contains the roots of the f(x) = x^{2} - 7x + 12? (3, 4), (4, 5), [2, 6] and [3, 4]?

**Summary:**

From among the options given, the roots of the equation f(x) = x^{2} - 7x + 12 lies in the intervals [2, 6] and [3, 4] both.

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