Math, asked by gamermobile550, 1 year ago

if p and q are zeroes of polynomial f(x)=2x^2-7x=3 find the value of p^2 +q^2

Answers

Answered by lublana
4

Given polynomial is  f(x)=2x^2-7x+3

Compare with standard quadratic  ax^2+bx+c , we get

a=2, b=-7, c=3

We know that sum of roots is given by (-b/a)

so the sum is -(-7)/2 or 7/2

since p and q are the zeros then we can write

p+q=7/2...(i)

product of roots is given by c/a so we get 3/2

which produces equation pq=3/2...(ii)

now we will try to find value of  p^2+q^2 using some rearrangements.

 p^2+q^2

 = p^2+q^2+2pq - 2pq

 = (p^2+q^2+2pq) - 2pq

 = (p+q)^2 - 2pq

Now plug the values from (i) and (ii)

 = (7/2)^2 - 2(3/2)

 = 49/4 - 3

 = 49/4 - 3*(4/4)

 = 49/4 - 12/4

 = 37/4

So the final answer is 37/4.

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