Question

if alpha and beta are the zeros of polynomial 2x2 - 5x + 8 then find the value of alpha 2 + beta 2​

Answer 1

α and β are the zeros of polynomial

2x² - 5x + 8 = 0

compare with ax² bx + c = 0

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

x = [ -(-5) +- √[(-5)² - 4(2)(8) ] ] / 2 × 2

x = [ 5 +- √( 25 - 16) ] / 4

x = ( 5 +- √9 )/ 4 = (5 +- 3 )/ 4

•°• α = (5 + 3)/4 and β = (5 - 3) / 4

now, α2 = 2(5 + 3)/4 and β2 = 2(5 - 3)/4

α2 = (5 - 3)/2 and β2 = (5 - 3)/2 is Answer

Answer 2

Answer:The value of α+β is -5

Step-by-step explanation: Since we have given that  

Let α and β are the zeroes of the above quadratic equation.  

As we know the relation between zeroes and the coefficients of quadratic equation in the form of ax²+bx+c=0

Hence, the value of α+β is -5.

                                                                                                                                                             

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