Question

Find the zeroes of the quadratic polynomial and verify the relationship between the zeroes and the coefficients; (A) a. 3√2x^2 + 13x + 6√2 b. 4√5x^2- 24x - 9√5

Answer 1

Answer:

3√2 x² + 13 x + 6√2

= 3√2 x² + 9x + 4x + 6√2

= 3x(√2 x + 3) + 2√2(√2x + 3)

= (√2x + 3)(3x + 2√2)

Zeroes of the polynomial:

(3x + 2√2) = 0

⇒ x = 2√2/3

(√2x + 3) = 0

⇒ x = -3/√2

Sum of the roots = 2√2/3 -3/√2 = -13/3√2

Product of the roots = 2√2/3 × 3/√2 = 2

Sum of the roots = -b/a = -13/3√2

Product of the roots = c/a = 6√2 / 3√2 = 2.

Answer 2

Step-by-step explanation:

3√2 x² + 13 x + 6√2

= 3√2 x² + 9x + 4x + 6√2

= 3x(√2 x + 3) + 2√2(√2x + 3)

= (√2x + 3)(3x + 2√2)

Zeroes of the polynomial:

(3x + 2√2) = 0

⇒ x = 2√2/3

(√2x + 3) = 0

⇒ x = -3/√2

Sum of the roots = 2√2/3 -3/√2 = -13/3√2

Product of the roots = 2√2/3 × 3/√2 = 2

Sum of the roots = -b/a = -13/3√2

Product of the roots = c/a = 6√2 / 3√2 = 2.