If alpha and beta are the zeroes of the quadratic polynomial x^2 - 7x - 18, then find the value of alpha^2+ ß^2?
Answers
Answered by
1
Step-by-step explanation:
alpha + beta = 7
alpha beta = -18
alpha² + beta²
= (alpha + beta)² - 2alpha*beta
= (7)² - 2(-18)
= 49 + 36
= 85
Answered by
3
Given:
- Polynomial :- x² -7x -18
- α and β are zeroes of the polynomial.
To find:
The value of α² + β²
Solution:
Comparing with standard form
ax² + bx +c =0
So,
a = 1
b = -7
c = -18
Now,
We know that
Therefore,
Also,
So,
Now using identity we will find the value of a²+b²
(a + b)² = a² + b² +2ab
=> a² + b² = (a + b)² -2ab
Similarly,
α² + β² = ( α+β )² -2αβ
Substituting values
α²+β² = (7)² -2(-18)
= 49 + 36
Hence, the value of α² + β² = 85
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