Ls,28, Gven that α and β are the roots of the equation x2-7x + 4,α(

1.	Ls,28, Gven that α and β are the roots of the equation x2-7x + 4,α() show that α3-53a + 28(ii) find the value of+
Answer» :aandßare the roots of the equation x2= 7x+ 4 i.e. x2– 7x– 4 = 0. now a should satisfy the equation.. as it is a root of the equation..so ⇒a2– 7a+ 4 = 0 ⇒ (a– 7) (a2– 7a–4) = 0 ⇒a3– 7a2– 4a+7a2–49a– 28 = 0 ⇒a3– 53a– 28 = 0 ⇒a3= 53a + 28 here sum of roots = a+ß = 7 and aß = -4 so, a/ß +ß/a = (a²+ß²)/(aß) = (a+ß)²-2aß/(aß) = ((7)²-2*4)/(4) = (49-8)/4 = 41/4

Ls,28, Gven that α and β are the roots of the equation x2-7x + 4,α() show that α3-53a + 28(ii) find the value of+

Answer»

:aandßare the roots of the equation

x2= 7x+ 4 i.e.

x2– 7x– 4 = 0.

now a should satisfy the equation.. as it is a root of the equation..so ⇒a2– 7a+ 4 = 0

⇒ (a– 7) (a2– 7a–4) = 0

⇒a3– 7a2– 4a+7a2–49a– 28 = 0

⇒a3– 53a– 28 = 0

⇒a3= 53a + 28

here sum of roots = a+ß = 7 and aß = -4

so, a/ß +ß/a = (a²+ß²)/(aß) = (a+ß)²-2aß/(aß) = ((7)²-2*4)/(4) = (49-8)/4 = 41/4