Question

a and ß are the o of the quadratic
Polynomial x²-px+q then find the value of
alpha² +beta²​

Answer 1

Answer:

p²

Step-by-step explanation:

Given a and ß are the o of the quadratic

Polynomial x²-px+q

a= 1 b=-p c= q

then

a + ß = -b/a

= -(-p)/1

=+p

then,

alpha² +beta²

=(a+ ß)²

=(+p)²

=p²

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Answer 2

Step-by-step explanation:

Consider the given polynomial

f(x)=x

2

−px+q

α and βare the zeros of given polynomial

We know that,

Sumofzeros=−

cofficentofx

2

cofficentofx

α+β=

1

−(−p)

α+β=p

Productofzeros=

cofficentofx

2

constant

α×β=

1

q

α×β=q

Then,

Part (1):-

α

2

+β

2

=(α+β)

2

−2αβ

α

2

+β

2

=p

2

−2q

Part (2):-

α

1

+

β

1

=

αβ

α+β

=

q

p

Hence, this is the answer.

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