Question

alpha,beta are zeraes of 3x square - 5x + 6=0 then alpha square + beta square​

Answer 1

Answer:

- 11 / 36

Step-by-step explanation:

α, β are the roots of equation 3x² - 5x + 6 = 0

Comparing 3x² - 5x + 6 = 0 with ax² + bx + c = 0 we get,

• a = 3
• b = - 5
• c = 6

Sum of roots = α + β = - b / a = - ( - 5 ) / 3 = 5 / 3

Product of roots = αβ = c / a = 6 / 3

Using algebraic identity ( α + β )² = α² + β² + 2αβ

⇒ ( 5 / 3 )² = α² + β² + 2( 6 / 3 )

⇒ 25 / 9 = α² + β² + 12 / 3

⇒ 25 / 9 - 12 / 3 = α² + β²

⇒ ( 25 - 36 ) / 36 = α² + β²

⇒ - 11 / 36 = α² + β²

Therefore the value of α² + β² is - 11 / 36.