Question

If alpha , beta are the zeros of the polynomial ax2 +bx + c , then (A2+b2)=

Answer 1

Answer:

If p and q are the zeroes of quadratic polynomial ax²+bx+c then evaluate p-q.

Given:

p and q are the zeroes of quadratic polynomial ax²+bx+c.

To Find:

The value of p-q.

Solution:

1) If p and q are the zeros of the polynomial the there is a relation between the zeros and the coefficient of the quadratic polynomial.

2) Sum of the roots = p+q= −b/a = −(coefficient of x) / (coefficient of x²)

Product of the toots = pq = c/a = (coefficient of x) / (coefficient of x²)

3) To find p-q we have to find the square of the first expression.

(p+q)²= (−b/a)²                                                          

p² + q² + 2pq = b²/a²

p² + q² + 2pq - 4pq = b²/a² - 4pq (Subtract 4pq form both side)

p² + q² - 2pq = b²/a² - 4c/a

(p-q)² = (b² - 4ac) / a²

(p-q) = √[(b² - 4ac) / a²]

(p-q) = √(b² - 4ac) / a

The value of  (p-q) = √(b² - 4ac) / a