Question

• Obtain all zeros of the polynomial f(x) = 2x^4 + x^3 - 14x^2 - 19x - 6, if two of it's zeros are -2 and -1.

Chapter - Polynomial
Class - X​

Answer 1

GIVEN :

Polynomial : f(x) = 2x⁴ + x³ - 14x² - 19x - 6

Zeroes : -2 and -1

= (x + 2) (x + 1)

= x(x + 1) + 2(x + 1)

= x² + x + 2x + 2

= x² + 3x + 2

Divide the polynomial with x² + 3x + 2

The quotient is 2x² - 5x - 3

Split the middle term

2x² - 5x - 3

2x² - 6x + x - 3

2x(x - 3) + 1(x - 3)

x - 3 = 0 2x + 1 = 0

2x = -1

x = 3 and x = -1/2

Therefore, the other zeroes are 3 and -1/2.