Question

if a and b are the zeros of polynomial 2x2-5x+8evaluate b2+a2

Answer 1

Heya !!




2x² - 5x + 8




Here,



A = 2 , B = -5 and C = 8.






Sum of zeroes = -B/A



a + b = 5/2 ------(1)



And,


Product of zeroes = C/A



a × b = 8/2


a × b = 4 -----(2).






---------------------------------



a² + b²



=> ( a + b )² - 2ab




=> (5/2)² - 2 × 4




=> 25/4 - 8



=> 25 - 32/4




=> -7/4.

Answer 2

$\textbf{Hey!!}$

$\textbf{2x{}^{2} - 5x + 8}$

On comparing with $\textbf{ax{}^{2} + bx + c}$

a = 2 , b = - 5 , c = 8

Sum of zeroes = - b / a

$= > \alpha + \beta = \frac{5}{2}$

Product of zeroes = c / a

$= > \alpha \beta = 4$

$a {}^{2} + b {}^{2} \\ \\ = (a + b) {}^{2} - 2ab \\ \\ = (\frac{5}{2}) {}^{2} - 2(4) \\ \\ = \frac{25}{4} - 8 \\ \\ = \frac{25 - 32 \ }{4} \\ \\ = \frac{ - 7}{4}$

$\textbf{Answer}$

$\boxed{\frac{-7}{4}}$