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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Which of the intervals contains the roots of the f(x) = x2 - 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) = x2 - 7x + 12
⇒ f(x) = x2 - 7x + 12
⇒ f(x) = x2 - 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) = x2 - 7x + 12 lies in the intervals [2, 6] and [3, 4] both.
Which of the intervals contains the roots of the f(x) = x2 - 7x + 12? (3, 4), (4, 5), [2, 6] and [3, 4]?
Summary:
From among the options given, the roots of the equation f(x) = x2 - 7x + 12 lies in the intervals [2, 6] and [3, 4] both.
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