Question

2x²+5x +2=0 root of this equation are p and q find the equation of which roots are p+q and 1/2pq​

Answer 1

Answer:

Here we know that if a quadratic equation is given we can find the sum of its roots and products .

so by formula

sum of roots =-b/a

product of roots =c/a

for the equation ax^2 +bx+c

now by formula the sum of roots is

p+q=-5/2

product pq=2/2=1

now we have to find a equation having roots p+q

and 1/2pq

,Now we know that if we have to make the quadratic equation by give roots in variable x general form is

x^2 -(sum of roots ) x+ product of roots

so x^2 -(p+q+1/2pq)x + (p+q)(1/2pq). -(1)

putting all values in (1)

x^2-( -5/2+1/2) x+(-5/2)(1)

x^ 2+2x -5/2

required ans is

2x^2+4x-5