Question

If the zero of the polynomial x square - Px plus q are three and two then find the value of p and q

Answer 1

Question

If the zeroes of the polynomial ${x}^2 - px + q = 0$ are three and two respectively.

Then find the value of p and q .

Solution

In the above question, the following information is given -  

The zeroes of the polynomial ${x}^2 - px + q = 0$ are three and two respectively.

$\sf { Let \: the \ required \ Zeroes \ be \ \alpha \ and \ \beta \ respectively. } \\ \\ \tt{ According \ to \ the \ above \ question - } \\\\\alpha + \beta = 3 + 2 = 5\\\\ \sf{ The \ required \ Sum \ Of \Zeroes = \dfrac{ p}{1} = p } \\\\Hence \\\\p = 3 \\\\\sf{ Product \ Of \ Zeroes = \alpha \times \beta = 2 \times 3 = 6 } \\\\\sf{ But , Product \ Of \ Zeroes = \dfrac{c}{a} = q . } \\\\Hence \\\\q = 6$

Answer 2

Given: The zeros of the polynomial x² - px + q are 3 and 2.

To find: The value of p and q.

Answer:

We know that the general form of a quadratic question is:

$\tt x^2\ -\ (sum\ of\ the\ zeros)x\ +\ (product\ of\ the\ zeros)$

Comparing the given equation with the general form, we get that the sum of the zeros is p and the product is q.

Let's take a sample equation.

ax² + bx + c

From this, the sum of the zeros is -b/a and the product is c/a.

Since 3 and 2 are the zeros,

Sum of the zeros ⇒ 3 + 2 = 5 = p

Product of the zeros ⇒ 3*2 = 6

Therefore, p = 5 and q = 6.