The equation 2x2-xFind the values of:0 has roots α and β.(a) α2 + �

1.	The equation 2x2-xFind the values of:0 has roots α and β.(a) α2 + β2(b) +α(c) α4β4
Answer» sum of root a+b = -(-1/2) = 1/2 product of roots = ab = -2/2 = -1 so, a²+b² = (a+b)²-2ab = (1/2)²-2(-1) = 1/4+2 = 9/4 a/b +b/a = (a²+b²)/ab = -9/4 a⁴+b⁴ = (a²+b²)²-2a²b² = (9/4)²-2(a²b²)² = 81/16-2(1)= 67/16

The equation 2x2-xFind the values of:0 has roots α and β.(a) α2 + β2(b) +α(c) α4β4

Answer»

sum of root a+b = -(-1/2) = 1/2 product of roots = ab = -2/2 = -1

so, a²+b² = (a+b)²-2ab = (1/2)²-2(-1) = 1/4+2 = 9/4

a/b +b/a = (a²+b²)/ab = -9/4

a⁴+b⁴ = (a²+b²)²-2a²b² = (9/4)²-2(a²b²)² = 81/16-2(1)= 67/16