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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 following is a polynomial with roots: - square root of 5, square root of 5, and -3?
x3 - 2x2 - 3x + 6
x3 + 2x2 - 3x - 6
x3 - 3x2 - 5x + 15
x3 + 3x2 - 5x - 15
Solution:
Given: -square root of 5, square root of 5, and -3
If a polynomial contains root b, then (x - b) is the factor of a polynomial.
It can be written as
-√5, √5 and -3
y = (x - (-√5)) (x - √5) (x + 3)
y = (x + √5)(x - √5)(x + 3)
Using the algebraic identity a2 - b2 = (a + b)(a - b)
y = (x2 - 5)(x + 3)
By further calculation,
y = x3 + 3x2 - 5x - 15
Therefore, the polynomial is x3 + 3x2 - 5x - 15.
Which of the following is a polynomial with roots: -square root of 5, square root of 5, and -3?
Summary:
The polynomial with roots -square root of 5, square root of 5, and -3 is x3 + 3x2 - 5x - 15.
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