Question

5. If one zero of the polynomial q(x) = x2 + px + 8 is
double the other, then find the value of p and hence
both zeroes of q(x).​

Answer 1

Answer:

2x

2

−5x−3=0

2x

2

−6x+x−3=0

(x−3)(2x+1)=0

x=3,−

2

1

Now,

Zeroes of the polynomial x

2

−px+q are double in values to the zeroes of polynomial 2x

2

−5x−3.

Therefore,

Zeroes of polynomial x

2

−px+q will be- 6,−1

Therefore,

Sum of roots =

a

−b

6+(−1)=−(−p)

⇒p=5

Product of root =

a

c

6×−1=q

⇒q=−6

Hence the values of p and q are 5 and −6 respectively.