Question

if the zeroes of the polynomial x3-6x2+x+2 are p-q, p and p+q .Find the values p and q

Answer 1

Answer:

$p = 2, q = \sqrt{5}$ or $p = 2, q = -\sqrt{5}$

Step-by-step explanation:

The sum of roots p - q, p and p + q is: p - q + p + p + q = 3p, which, for a polynomial, is given by -b/a.

So, 3p = -(-6)/1 = 6

So, p = 2.

Now, product of the roots is: $(p - q)p(p + q) = p(p^2 - q^2)$

Found: p = 2, so:

$2(4 - q^2)$

Now, product of roots is given by, here, -(2)/1 = -2.

So, $2(4 - q^2) = -2$

Therefore: $4 - q^2 = -1 => q^2 = 5$

So, $q = \sqrt{5}$ or $q = -\sqrt{5}$