P(x) = 2x² - 5x - 6 ... 👉👉a + b = 5/2 and ab = -6/2 = -3 .... 👉👉equation having a+b & ab as its roots is :- x² - [(a+b) + (ab)]x + (a+b)(ab) = 0i.e, x² - [5/2 - 3]x + (5/2)(-3) = 0 i.e, x² + (1/2)x - (15/2) = 0i e, 2x² + x - 15 = 0

**Quadratic Polynomial:**

A quadratic polynomial is a polynomial of degree 2, which can be expressed in the form ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

**Zeros of a Quadratic Polynomial:**

The zeros of a quadratic polynomial are the values of x for which the polynomial becomes zero. In other words, if a quadratic polynomial P(x) has zeros a and b, then P(a) = 0 and P(b) = 0.

**Given Quadratic Polynomial:**

Let's consider the given quadratic polynomial as P(x) = 2x^2 - 5x - 6.

**Finding the Zeros:**

To find the zeros of the given quadratic polynomial, we set P(x) equal to zero and solve for x:

2x^2 - 5x - 6 = 0

To factorize this quadratic expression, we need to find two numbers whose product is -12 and sum is -5. The numbers -8 and 3 satisfy these conditions:

2x^2 - 8x + 3x - 6 = 0

2x(x - 4) + 3(x - 2) = 0

(x - 4)(2x + 3) = 0

So, the zeros of the given quadratic polynomial are x = 4 and x = -3/2.

**Forming a Quadratic Polynomial with the Given Zeros:**

To form a quadratic polynomial with zeros a, b, and ab, we use the fact that the sum and product of the zeros of a quadratic polynomial are related.

For the given quadratic polynomial, the zeros are a = 4 and b = -3/2. The product of the zeros is ab = 4 * (-3/2) = -6.

So, the quadratic polynomial with zeros a, b, and ab can be written as:

P(x) = k(x - a)(x - b)(x - ab)

We can substitute the values of a, b, and ab to get the specific quadratic polynomial:

P(x) = k(x - 4)(x + 3/2)(x + 6)

Here, k is a constant that can take any non-zero value.

Therefore, the quadratic polynomial with zeros 4, -3/2, and -6 is P(x) = k(x - 4)(x + 3/2)(x + 6).