1.

If α and β are the roots of equation 7x2 + 4x – 1 = 0, then find the value of (α2 + β2)?1. 15/492. 30/493. 16/494. 25/49

Answer» 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


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