Question

ii) Given a quadratic equation x2 + px +q = 0. Determine p and q so that the roots of the equation are p and q​

Answer 1

Answer:

The values of p and q are 1/2 or -1 and 1/2 or 2 respectively

Step-by-step explanation:

x^2+px-q=0

Considering p as root (1)

Now considering q as root (2)

Now from (1)

Now from (2)

p+q=1

Considering p as 1/2

Considering p as -1

p+q = 1

-1 + q = 1

q = 1+1

q = 2

Answer 2

Step-by-step explanation:

x²+px+q=0

Considering p as root

=p²+p(p)-q=0

=p²+p²-q=0

=2p²-q=0

q=2p².......(1)

Now consider q as root

=q²+pq-q=0

=q(q+p-1)=0

p+q=1.........(2)

From (1)

=p+2p²=1

=2p²+p-1=0

=2p²+2p-p-1=0

=2p(p+1)-1(p+1)=0

=(2p-1) (p+1)=0

=2p-1=0 or p+1=0

=p=1/2 or p=-1

Now from (2)

=p+q=1

Considering p as 1/2

=1/2+q=1

=q=1-1/2

=q=1/2

Considering p as -1

=p+q=1

=-1+q=1

=q=1+1

=q=2

Ans: The value of p and q are 1/2 or -1 and 1/2 or 2

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