Question

0.4
If a and B are the zeros of the quadratic polynomial f(x)=ax²+bx+c, then evaluate
(1)a²+ B²
(2) a²/b+b²/a
(3)a³+b³
(4)1/a³+1/b³
(5)a/b+b/a​

Answer 1

Answer:

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}= > (a−b)

2

=

a

2

b

2

−

a

4c

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

2

=

a

2

b

2

−4ac

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

a

b

2

−4ac

,−

a

b

2

−4ac