Question

step by step explanation plzzz​

Answer 1

Answer:

37/4

Step-by-step explanation:

Given : 2x² - 7x + 3

Given that p and q are the zeroes of the above polynomial.

Using Middle Term Factorisation, we get

→ 2x² - 6x - x + 3

→ 2x(x - 3) - 1(x - 3)

→ (2x - 1)(x - 3)

To find zeroes, each factor should be equal to zero.

Hence,

2x - 1 = 0 and x - 3 = 0

→ x = 1/2 and x = - 3

A.T.Q., p = 1/2 and q = - 3

Now,

Value of p² + q² :

→ (1/2)² + (- 3)²

→ 1/4 + 9

→ [ 1 + 9(4) ] / 4

→ [ 1 + 36 ] / 4

→ 37/4

Answer 2

$\bf Given:\ \sf p\ and\ q\ are\ the\ zeroes\ of\ the\ polynomial\ 2x^2\ -\ 7x\ +\ 3.\\\\\\\bf To\ find:\ \sf The\ value\ of\ p^2\ +\ q^2.\\\\\\\bf Answer:\ \\\\\\\sf Let's\ suppose\ ax^2\ +\ bx\ +\ c\ is\ an\ equation.\\\\\\Then,\ the\ sum\ of\ its\ zeroes\ will\ be\ \dfrac{-b}{a}.\\\\\\Its\ product\ will\ be\ \dfrac{c}{a}.\\\\\\From\ the\ given\ equation,\ \\\\\\a\ =\ 2,\ b\ =\ -7\ and\ c\ =\ 3.\\\\\\According\ to\ the\ question,\ p\ and\ q\ are\ the\ zeroes.\ Hence,$

$\tt p\ +\ q\ =\ \dfrac{7}{2}.\\\\\\p\ \times\ q\ =\ \dfrac{3}{2}.\\\\\\\sf Now, \we\ know\ that\ (p\ +\ q)^2\ =\ p^2\ +\ 2pq\ +\ q^2.\\\\\\Using\ the\ values\ we\ have,\\\\\\\bigg(\dfrac{7}{2}\bigg)^2\ =\ p^2\ +\ q^2\ +\ 2\ \times\ \dfrac{3}{2}\\\\\\\dfrac{49}{4}\ =\ p^2\ +\ q^2\ +\ 3\\\\\\\dfrac{49}{4}\ -\ 3\ =\ p^2\ +\ q^2\\\\\\\dfrac{49\ -\ 12}{4}\ =\ p^2\ +\ q^2\\\\\\\bf \dfrac{37}{4}\ =\ p^2\ +\ q^2.$