Question

If alpha and beta are the zeroes of the polynomial 2y 2 + 7y+5 find the value of alpha 2 and beta 2 .

Answer 1

[tex]= 2 y^{2} + 7y +5 [/tex]
We know that : 
         $\alpha + \beta = \frac{-b}{a} \\ \\ \alpha + \beta = \frac{-7}{2}$
Further:
          $\alpha \beta = \frac{c}{a} \\ \\ \alpha \beta = \frac{5}{2}$

Now, we need:
         $\alpha ^{2} + \beta ^{2} = ( \alpha + \beta )^{2} -2 \alpha \beta \\ \\ \alpha ^{2} + \beta ^{2} = ( \frac{-7}{2}) ^{2} - 2( \frac{5}{2}) \\ \\ \alpha ^{2} + \beta ^{2}= \frac{49}{4}-5 \\ \\ \alpha ^{2} + \beta ^{2}= \frac{49-20}{4} \\ \\ \alpha^{2}+ \beta ^{2} = \frac{29}{4}$