Question

If α and β are the roots of the equation 3x² – 7x + 2 = 0, then find the value of α² + β².
1. 35/9
2. 82/9
3. 37/9
4. 49/9

Answer 1

Correct Answer - Option 3 : 37/9

Given:

α and β are the roots of the equation 3x² – 7x + 2 = 0

Formula Used:

If ax² + bx + c = 0, then

Sum of the roots = -(b/a)

Product of the roots = (c/a)

a² + b² = (a + b)² – 2 × a × b

Calculation:

For equation, 3x² – 7x + 2

a = 3, b = -7, and c = 2

Sum of the roots = -(b/a)

⇒ α + β = -(-7/3)

⇒ α + β = 7/3     

Product of the roots = (c/a)

⇒ α × β = 2/3     

Also, α² + β² = (α + β)² – 2 × α × β

⇒ (7/3)² – 2 × (2/3)

⇒ (49/9) – (4/3)

⇒ (49 – 12)/9

⇒ 37/9

∴ The value of α² + β² is 37/9.