Question

If p and q are the roots of x2-x+1 =0 find the value of p2+q2 and p3+q3

Answer 1

Answer:

p² + q² = -1

p³ +q³ = -2

Step-by-step explanation:

for eq ax² + bx + c = 0

Sum of roots = -b/a

Multiplication of roots = c/a

x² - x + 1 = 0

p & q are roots

a =1 , b =-1 c ,1

p+q = -(-1)/1 = 1

pq = 1/1 = 1

(p+q)² = p² + q² + 2pq

=> 1² = p² + q² + 2×(1)

=> p² + q² = 1-2

=> p² + q² = -1

(p+q)³ = p³ + q³ + 3pq(p+q)

=> 1³ = p³ +q³ + 3×1×1

=> p³ +q³ = 1 - 3

=> p³ +q³ = -2

Answer 2

sum of zero=-b/a(as p and q are two roots.)

p+q=-(-1)/1=1

and, product of zero=c/a

pq=1/1=1

now,p2+q2=(p+q)Sq -2pq

=(1)sq-2×1=-1

and, p3+q3=(p+q)(p2+q2-pq)

=1 (-1-1)=-2

hope it will help you if yes then mark it as brainlist.