Question

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

Answer 1

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.