Given that √2 is a zero of the cubic polynomial 6x³ + √2x² - 10x - 4√2 , find its other two zeroes
Solution:
Given, the cubic polynomial is 6x³ + √2x² - 10x - 4√2.
One of the zeros of the polynomial is √2.
We have to find the other two zeros.
By using long division,
On factoring 6x² + 7√2x + 4,
6x² + 4√2x + 3√2x + 4 = 0
2x(3x + 2√2) + √2(3x + 2√2) = 0
(2x + √2)(3x + 2√2) = 0
Now, 2x + √2 = 0
2x = -√2
x = -√2/2
x = -1/√2
Also, 3x + 2√2 = 0
3x = -2√2
x = -2√2/3
Therefore, the zeros of the polynomial are √2, -1/√2 and -2√2/3.
✦ Try This: Given that -1/√2 is a zero of the cubic polynomial 6x³ + √2x² - 10x - 4√2 , find
its other two zeroes
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2
NCERT Exemplar Class 10 Maths Exercise 2.4 Problem 3
Given that √2 is a zero of the cubic polynomial 6x³ + √2x² - 10x - 4√2 , find its other two zeroes
Summary:
Given that √2 is a zero of the cubic polynomial 6x³ + √2x² - 10x - 4√2 , its other two zeroes are √2, -1/√2 and -2√2/3.
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