Question

Α' β

Answer 1

Answer:

8x² +36x -27=0

Step-by-step explanation:

2x²= 6x +3

Let's rewrite the equation into the form of ax²+bx+c= 0.

2x² -6x -3=0

Thus, a= 2

b= -6

c= -3

Sum of roots= $- \frac{b}{a}$

Since your roots are p and q, sum of roots= p +q

p +q= $- (\frac{ - 6}{2} )$

p +q= 6 ÷2

p +q= 3

Product of roots= $\frac{c}{a}$

pq= $- \frac{3}{2}$

Quadratic equations:

x² -(sum of roots)x +(product of roots)= 0

Thus, we have to find the sum and the product of the new roots, p²q and pq².

p +q= 3

pq= -3/2

Product of new roots

= (p²q)(pq²)

= p³q³

= (pq)³

$= ( - \frac{3}{2} )^{3} \\ = - \frac{27}{8}$

sum of new roots

= p²q +pq²

= pq(p +q)

= (-3/2)(3)

= -9/2

Thus, the quadratic equation with roots p²q and pq² is

x² -(-9/2)x -27/8 = 0

$x ^{2} + \frac{9}{2} x - \frac{27}{8} = 0$

Multiply by 8 throughout:

$8 {x}^{2} + 36x - 27 = 0$