Question

if bracket X - 3 bracket close and Bracket x minus one upon 3 bracket close are both factors of x square + 5 x + b show that a equal to b
​

Answer 1

Let f(x) = ax^2 + 5x + b;

Then, (x-3) and (x - 1/3) are the factors of f(x).

Thus, f(3) = 9a +15+b = 0 .....(1)

And, f(1/3) = a/9 + 5/3 + b = 0

Hence, 9a + 15 + b = a/9 + 5/3 + b

or, 80/9 a = -40/3

or, a = -40/3 × 9/80

$\: \: \: \: a = \frac{ - 3}{2}$

Substituting the value of a in (1), we get;

-27/2 + 15 + b = 0

or, b = 0 - 3/2

$\: \: \: \: b = \frac{ - 3}{2}$

Hence, it is proved that

$a = b = \frac{ - 3}{2}$

HOPE THIS COULD HELP!!!