Question

If p and q are the zeroes of the quadratic polynomial x²+mx+n²+a find p²+q²+pq.

a. 0
b. a
c. -a
d. m or -m
​

Answer 1

Sum of zeroes/roots p+q=-m____(1)

Product of zeroes p*q=n^2____(2)

Squaring equation (1) on both sides,

p^2 + q^2 + 2pq = m^2_____(3)

Substituting value of p*q from equation (2) in (3)

p^2 + q^2 + 2n^2 =m^2

Therefore, p^2 + q^2 =m^2 - 2n^2

So value of p^2 + q^2 +pq

=m^2 - 2n^2 +n^2 (since pq=n^2 from (2) )

=m^2 - n^2 or

=(m+n)(m-n)

And you can also solve this as shown in picture

hope this will help you....

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