Write the coefficient of x² of the following : (2x - 5) (2x² - 3x + 1)
Solution:
Given, the polynomial is (2x -5) (2x² - 3x + 1)
We have to find the coefficient of x²
By multiplicative and distributive property,
(2x - 5) (2x² - 3x + 1) = 2x(2x²) - 2x(3x) + 2x(1) - 5(2x²) + 5(3x) - 5(1)
= 4x³ - 6x² + 2x - 10x² + 15x - 5
= 4x³ - 6x² - 10x² + 2x + 15x - 5
= 4x³ - 16x² + 17x - 5
4x³ - 16x² + 17x - 5 is a cubic polynomial with the highest degree of exponent as three.
Therefore, the coefficient of x² is -16.
✦ Try This: Write the coefficient of x² of the following : x² + 3x/2 = 1/4
Given, the polynomial is x² + 3x/2 = 1/4
We have to find the coefficient of x²
Rearranging the polynomial,
x² + 3x/2 - 1/4 = 0
4x² + 6x - 1 = 0
4x² + 6x - 1 is a quadratic polynomial with the highest degree of exponent as two.
Therefore, the coefficient of x² is 4.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.3 Problem 4(iv)
Write the coefficient of x² of the following : (2x - 5) (2x² - 3x + 1)
Summary:
A polynomial expression has terms connected by the addition or subtraction operators. The coefficient of x² in (2x - 5) (2x² - 3x + 1) is -16
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