Question

3. Compute the zeroes of the polynomial 4x2 – 4x – 8. Also, establish a relationship between the zeroes and coefficients.​

Answer 1

To Find :-

• A relationship between the zeroes and coefficients.

Solution :-

Given,

• The zeroes of the polynomial 4x² - 4x - 8.

Let, the given polynomial be p(x) = 4x² - 4x - 8.

Taking, p(x) = 0

⟶ 4x² - 4x - 8 = 0

⟶ 4(x² - x - 2) = 0

⟶ x² - x - 2 = 0

⟶ x² - 2x + x - 2 = 0

⟶ x(x - 2) + 1(x - 2) = 0

⟶ (x - 2)(x + 1) = 0

⟶ x = 2 OR x = -1

Since, the roots of given polynomial is -1 and 2.

Now,

Relation between the sum of zeroes and coefficients,

⟶ -1 + 2 = (- coefficient of x)/(coefficient of x²)

⟶ -1 + 2 = -(-4)/4

⟶ 1 = 1

Relation between the product of zeroes and coefficients,

⟶ -1 × 2 = (constant)/(coefficient of x²)

⟶ -1 × 2 = -8/4

⟶ -2 = -2

Hence, relationship is verified!!