Question

Find the zeros of the quadratic polynomial 6x square -3 -7x and verify the relationship between the zeros and the coefficients of polynomial

Answer 1

Hey!

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Quadratic polynomial - 6x ^2 - 3 - 7x
= 6x^2 - 7x - 3

Splitting the middle term -

6x^2 - 9x + 2x -3

(6x^2 - 9x) + (2x - 3)

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

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

Zeroes of the polynomial -

3x + 1 = 0
3x = -1
x = -1/3

2x - 3 = 0
2x = 3
x = 3/2

Zeroes are -1/3 and 3/2

Verifying the relationship between the zeroes and the coefficients -:

Sum of zeroes = -1/3 + 3/2 = 7/6
= Coefficient of x / Coefficient of x^2

Product of zeroes = -1/3 × 3/2 = -3/6
= Coefficient of constant /coefficient of x^2

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Hope it helps...!!!

Answer 2

Answer:

Step-by-step explanation:

Quadratic polynomial - 6x ^2 - 3 - 7x

= 6x^2 - 7x - 3

Splitting the middle term -

6x^2 - 9x + 2x -3

(6x^2 - 9x) + (2x - 3)

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

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

Zeroes of the polynomial -

3x + 1 = 0

3x = -1

x = -1/3

2x - 3 = 0

2x = 3

x = 3/2

Zeroes are -1/3 and 3/2

Verifying the relationship between the zeroes and the coefficients -:

Sum of zeroes = -1/3 + 3/2 = 7/6

= Coefficient of x / Coefficient of x^2

Product of zeroes = -1/3 × 3/2 = -3/6

= Coefficient of constant /coefficient of x^2