Question

If α and β are the zeros of the quadratic polynomial f (x) = x² - 5x +6, find the value of ( α²β + β²α ). 
1. 20
2. 30
3. 50
4. 60

Answer 1

Correct Answer - Option 2 : 30

Concept:

If α and β are the roots of equation , ax2 + bx + c =0 

Sum of roots (α + β) = \(\rm \frac{-b}{a}\)  

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

(x + y)2 = x2 + y2 + 2xy .

Calculation:

Given: f (x) = x2 - 5x + 6

Comparing f(x) with ax2 + bx + c =0 , we have , a = 1 , b= -5 and c=  6. 

Now, sum of roots =  α + β = \(\rm \frac{-b}{a}\) = \(\rm \frac{-(-5)}{1}\) = 5

And product of roots αβ = \(\rm \frac{c}{a}\) = \(\rm \frac{6}{1}\) = 6 . 

Now, α2β + β2α = αβ ( α+ β ) 

= 6 × 5 

= 30

The correct option is 2.