If α, β are the roots of the quadratic equation x² - 11x + 18 = 0, then the value of α² + β² is:

Question

Question

This question was previously asked in

RRB Group D 16 Sept 2022 Shift 1 Official Paper

Answer 1

Given:

x2 - 11x + 18 = 0

Concept Used:

For the standard form of quadratic equation,

ax² + bx + c = 0

Sum of roots = \(\frac{-b}{a}\)

Product of roots = \(\frac{c}{a}\)

Calculation:

Let the roots of the quadratic equation be α and β

In the given equation,

a = 1, b = –11, c = 18

Sum of roots = \(α+β=11\)

Product of roots = \(αβ=18\)

Squaring both sides of the sum of squares,

⇒ \((α+β)^2=(11)^2\)

⇒ \(α^2+β^2+2αβ=121\)

⇒ \(α^2+β^2+2\times 18=121\)

⇒ \(α^2+β^2=121-36=85\)

Therefore, the required value of α2 + β² is 85.

Hence, the correct answer is option 3).