A quadratic polynomial having zeroes 0 and - 2, is

A quadratic polynomial having zeroes 0 and - 2, is

The standard form of a quadratic polynomial when its zeroes are $\alpha$ and $\beta$ is:

$p(x) = k(x - \alpha)(x - \beta)$, where $k$ is a constant.

Given zeroes: $\alpha = 0$, $\beta = -2$

Substituting the values:

$p(x) = k(x - 0)(x + 2)$

$p(x) = kx(x + 2)$

$p(x) = k(x^2 + 2x)$

For simplicity, let $k = 1$:

$p(x) = x^2 + 2x$

• On combining two groups of students having 30 and 40 average marks respectively in an exam, the resultant group has an average score of 34. Find the ratio of the number of students in the first group to the number of students in the second group.
• Directions: Read the following and answer the questions that follow.There are 3 classes having 20, 25 and 30 students respectively having average marks in an examination as 20, 25 and 30 respectively. If the three classes are represented by A, B and C a
•  Bucket P has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill the empty drum. How many turns it will take for both the buckets P and Q, having each turn together to fill the emp
• Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively (i) $\frac{1}{4}, -1$ (ii) $\sqrt{2}, \frac{1}{4}$ (iii) $0, \sqrt{5}$ (iv) $1, 1$ (v) $- \frac{1}{4}, \frac{1}{4}$ (iv) $4, 1$
• If $\alpha, \beta$ are zeroes of the polynomial $8x^2 - 5x - 1$, then form a quadratic polynomial in $x$ whose zeroes are $\frac{2}{\alpha}$ and $\frac{2}{\beta}$