Question

If p and q are the zeroes of the polynomial x^2+ 7x +7 ,then form a quadratic polynomial whose zeroes are 2p and 2q

Answer 1

-b/a = p+q
p+q = -7/1
now 2p+2q = 2(p+q) = 2(-7) = -14

c/a = pq
pq = 7/1
now 2p2q = 4pq = 4(7) = 28

we observe a =1, b = -14, c = 28

New polynomial = $x^{2} -14x+28 = 0$ has zeroes 2p and 2q

Answer 2

Given :  p and q are the zeroes of a polynomial x² + 7x+7  

To Find :  form a polynomial whose zeroes 2p and 2q.​

Solution:

 p and q are the zeroes of a polynomial x² + 7x+7  

p + q  = Sum of zeroes = - 7/1 = - 7

pq = product of zeroes  = 7/1 = 7

a polynomial whose zeroes 2p and 2q.​

Sum of zeroes = 2p + 2q  = 2(p + q)  = 2 ( - 7)  = - 14

product of zeroes = 2p * 2q =  4pq  = 4( 7)  = 28

Hence a polynomial can be

x² -(- 14)x  + 28

= x² + 14x +  28  a polynomial whose zeroes 2p and 2q.​

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