Question

If α and β are the zeroes of the quadratic polynomial f(x) = ax² bx + c then evaluate :-

α-β

Answer 1

Given quadratic polynomial is ax² + bx + c
Given α, β are the zeroes of the given polynomial
α + β = ( – b/a)
αβ = (c/a)

Consider, (α - β)² = (α + β)² - 4 αβ
(α - β)² = (-b/a)² - 4(c/a)
(α - β)² = (b² - 4ac) / a²
(α - β) = ±(b² - 4ac)½ / a

I hope this answer helped you.

Answer 2

Given Quadratic polynomial is ax^2 + bx + c.

Let a, b be the zeroes of the given polynomial.

= > We know that Sum of zeroes = -b/a

         a + b = -b/a


= > We know that Product of zeroes = c/a

            ab = c/a


Now,

We know that By algebraic identity (a - b)^2 = (a + b)^2 - 4ab

 (a - b)^2 = (-b/a)^2 - 4(c/a)

$= \ \textgreater \ (a - b)^2 = \frac{b^2}{a^2} - \frac{4c}{a}$

$= \ \textgreater \ (a - b)^2 = \frac{b^2 - 4ac}{a^2}$

$= \ \textgreater \ (a - b) = + \frac{ \sqrt{b^2 - 4ac} }{a} , - \frac{ \sqrt{b^2 - 4ac} }{a}$




Hope this helps!