Question

Find non zero of values of p and q for which p and q are zeroes of x2
+px +q.

Answer 1

Given: The equation:  x2  + px + q .

To find: Non zero of values of p and q.

Solution:

• Now we have given that p and q are zeroes of the polynomial, so sum of roots are:

            p + q = -p / 1

            p + q = -p

            2p + q = 0

• And the product of the roots are:

            pq = q

            p = 1 ...................(i)

            putting (i)in sum of roots, we get:

            2(1) + q = 0

            q = -2

Answer:

          So the roots of the given equation are p = 1 and q = -2.

Answer 2

Given:  p and q are zeroes of x² +px +q

To find : non zero of values of p and q

Solution:

p and q are zeroes of x² +px +q

=> (x - p)(x - q) = x² +px +q

=> x² - (p + q)x  + pq  = x² +px +q

=>   - (p + q)x  + pq  =  px +q

=> pq  = q

Hence p = 1

& -(p + q) = p

=> -(1 + q) = 1

=> 1 + q = -1

=> q  = - 2

p = 1   & q  = -2

Lets verify

x²  + x  - 2 = 0

=> x² + 2x - x - 2 = 0

=> x(x + 2) - 1(x + 2) = 0

=> (x - 1)(x + 2) = 0

=> x = 1  , - 2

p = 1   & q  = -2

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