Question

if x1 and x2 are the roots of the equations ​

Answer 1

Answer:

B

Step-by-step explanation:

As x1x1, x2x2, x3x3 and x4x4 form GP then: x2=x1rx2=x1r, x3=x1r2x3=x1r2, x4=x1r3x4=x1r3, where rr is the common ratio.

Next: Viete's formula for the roots x1x1 and x2x2 of equation ax2+bx+c=0ax2+bx+c=0: x1+x2=−bax1+x2=−ba AND x1∗x2=cax1∗x2=ca.

For x2−3x+p=0=0x2−3x+p=0=0: (i) x1+x2=x1(1+r)=3x1+x2=x1(1+r)=3 AND (ii) x1∗x2=(x1)2∗r=px1∗x2=(x1)2∗r=p.

For x2−12x+q=0x2−12x+q=0: (iii) x3+x4=x1r2(1+r)=12x3+x4=x1r2(1+r)=12 AND x3∗x4=(x1)2∗r5=qx3∗x4=(x1)2∗r5=q.

From (i) 1+r=3x11+r=3x1 --> (iii) x1r2(1+r)=x1r2∗3x1=3r2=12x1r2(1+r)=x1r2∗3x1=3r2=12 --> r2=4r2=4 --> r=2r=2 (r=−2r=−2 is out as GP is increasing).

(x1)2∗r=2∗(x1)2=p(x1)2∗r=2∗(x1)2=p and (x1)2∗r5=32∗(x1)2=16p=q(x1)2∗r5=32∗(x1)2=16p=q. Only answer choice B satisfies this: 16*2=32.

Mark it as the BRAINLIEST answer