Question

If α and β are the roots of equation 7x² + 4x – 1 = 0, then find the value of (α² + β²)?
1. 15/49
2. 30/49
3. 16/49
4. 25/49

Answer 1

Correct Answer - Option 2 : 30/49

Given:

The given quadratic equation is 7x² + 4x – 1 = 0

Concept Used:

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

And product of roots (α × β) = c/a

Calculation:

By comparing the given quadratic equation 7x² + 4x - 1 with standard equation ax² + bx + c we can find the value of coefficient a, b and c

∴ a = 7, b = 4 and c = -1

Sum of roots (α + β) = -b/a = - (4)/7 = -4/7

And, product of roots (α × β) = c/a = -1/7

We know that,

α² + β² = (α + β) ² - 2(α × β)

⇒ α² + β² = (-4/7) ² - 2(-1/7) = 30/49