Question

if x =2 and x=3 are roots of 3x^2-2px+2q=0 tgen find p+q​

Answer 1

Given :

• Polynomial = 3x² - 2px + 2q = 0

• Two roots of this polynomial :-

• x = 2
• x = 3

To find :

• Value of p + q

Solution :

→ f(x) = 3x² - 2px + 2q = 0

→ x = 2

→ 3(2)² - 2p(2) + 2q = 0

→ 3(4) - 4p + 2q = 0

→ 12 - 4p + 2q = 0

→ 2q - 4p = - 12 -------(1)

→ f(x) = 3x² - 2px + 2q = 0

→ x = 3

→ 3(3)² - 2p(3) + 2q = 0

→ 3(9) - 6p + 2q = 0

→ 27 - 6p + 2q = 0

→ 2q - 6p = - 27 -------(2)

Solving (1) and (2) :-

2q - 4p = - 12

2q - 6p = - 27

(-)⠀(+)⠀⠀(+)

___________

→ 2p = 15

___________

→ 2p = 15

→ p = 15/2

→ p = 7.5

Substituting the value of x in equation (1) :-

→ 2q - 4p = - 12

→ 2q - 4(7.5) = - 12

→ 2q - 30 = - 12

→ 2q = 18

→ q = 18/2

→ q = 8

Therefore, the value of p = 7.5 and q = 8

→ p + q

→ 7.5 + 8

→ 15.5

Therefore, the value of p + q = 15.5