Write the coefficient of x2 in each of the following(i) (π/6)x + x2�

1.	Write the coefficient of x2 in each of the following(i) (π/6)x + x2 – 1(ii) 3x – 5(iii) (x –1) (3x – 4)(iv) (2x – 5) (2x2 – 3x + 1)
Answer» (i) (π/6) x + x²−1 (π/6) x + x²−1 = (π/6) x + (1) x²−1 The coefficient of x² in the polynomial (π/6) x + x²−1 = 1. (ii) 3x – 5 3x – 5 = 0x² + 3x – 5 The coefficient of x² in the polynomial 3x – 5 = 0, zero. (iii) (x – 1) (3x – 4) (x – 1)(3x – 4) = 3x² – 4x – 3x + 4 = 3x² – 7x + 4 The coefficient of x² in the polynomial 3x² – 7x + 4 = 3. (iv) (2x – 5) (2x² – 3x + 1) (2x – 5) (2x² – 3x + 1) = 4x³ – 6x² + 2x – 10x² + 15x– 5 = 4x³ – 16x² + 17x – 5 The coefficient of x² in the polynomial (2x – 5) (2x² – 3x + 1) = – 16

Write the coefficient of x2 in each of the following(i) (π/6)x + x2 – 1(ii) 3x – 5(iii) (x –1) (3x – 4)(iv) (2x – 5) (2x2 – 3x + 1)

Answer»

(i) (π/6) x + x²−1

(π/6) x + x²−1 = (π/6) x + (1) x²−1

The coefficient of x² in the polynomial (π/6) x + x²−1 = 1.

(ii) 3x – 5

3x – 5 = 0x² + 3x – 5

The coefficient of x² in the polynomial 3x – 5 = 0, zero.

(iii) (x – 1) (3x – 4)

(x – 1)(3x – 4) = 3x² – 4x – 3x + 4

= 3x² – 7x + 4

The coefficient of x² in the polynomial 3x² – 7x + 4 = 3.

(iv) (2x – 5) (2x² – 3x + 1)

(2x – 5) (2x² – 3x + 1)

= 4x³ – 6x² + 2x – 10x² + 15x– 5

= 4x³ – 16x² + 17x – 5

The coefficient of x² in the polynomial (2x – 5) (2x² – 3x + 1) = – 16