if a and B are the zeroes of the polynomials f(x) = x2 - px +q, find the value of a2 +B2
Answers
EXPLANATION.
a and b are the zeroes of the polynomial.
⇒ f(x) = x² - px + q.
As we know that,
Sum of the zeroes of the quadratic polynomial.
⇒ a + b = - b/a.
⇒ a + b = -(-p)/1 = p. - - - - - (1).
Products of the zeroes of the quadratic polynomial.
⇒ ab = c/a.
⇒ ab = q. - - - - - (2).
To find :
⇒ a² + b².
⇒ a² + b² = (a + b)² - 2ab.
⇒ a² + b² = (p)² - 2(q).
⇒ a² + b² = p² - 2q.
MORE INFORMATION.
Conjugate roots.
(1) = If D < 0.
One roots = α + iβ.
Other roots = α - iβ.
(2) = If D > 0.
One roots = α + √β.
Other roots = α - √β.
Answer:
a² + b² = p - 2q
Step-by-step explanation:
a , b be zeros of polynomial f(x) = x² - px + q
from polynomial ,
a = 1 , b = -p , c = q
sum of zeros = a + b = -b/a = -(-p)/1 = p → equation 1
product of zeros = ab = c/a = q/1 = q → equation 2
then ,
To find :
a² + b² = (a+b) - 2ab = p - 2(q) = p - 2q
- a² + b² = p - 2q