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if (x-root5) is a factor of x^3-3root5x^2-5x+15root5 , find all the zeros of the polynomial
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if (x-root5) is a factor of x^3-3root5x^2-5x+15root5 , find all the ze...
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if (x-root5) is a factor of x^3-3root5x^2-5x+15root5 , find all the ze...
Solution:
Given, (x-√5) is a factor of x³ - 3√5x² - 5x + 15√5.
It can be written as x³ - √5x² + √5x² - 3√5x - 5x + 15√5.
Taking common factor, we get x²(x - √5) + √5x(x - √5) - 5(x - √5).
(x - √5)(x² + √5x - 5) = 0.
Now, we have to solve x² + √5x - 5 = 0.
By using the quadratic formula, we get x = (-√5 ± √(25 + 20))/2
x = (-√5 ± √45)/2
x = (-√5 ± 3√5)/2, (-√5)/2.
Therefore, the zeros of the polynomial are -√5, (-√5 + 3√5)/2 and (-√5 - 3√5)/2.
Given, (x-√5) is a factor of x³ - 3√5x² - 5x + 15√5.
It can be written as x³ - √5x² + √5x² - 3√5x - 5x + 15√5.
Taking common factor, we get x²(x - √5) + √5x(x - √5) - 5(x - √5).
(x - √5)(x² + √5x - 5) = 0.
Now, we have to solve x² + √5x - 5 = 0.
By using the quadratic formula, we get x = (-√5 ± √(25 + 20))/2
x = (-√5 ± √45)/2
x = (-√5 ± 3√5)/2, (-√5)/2.
Therefore, the zeros of the polynomial are -√5, (-√5 + 3√5)/2 and (-√5 - 3√5)/2.
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if (x-root5) is a factor of x^3-3root5x^2-5x+15root5 , find all the zeros of the polynomial Related: Additional Questions Solution - Polynomials?
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