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If m and ( m + 4) are the roots of 4x24x15=0, f...

If m and ( m + 4) are the roots of 4x24x15=0, find the equation whose roots are 2 m and (2 m + 8)

A.

x2+8x15=0

B.

x22x15=0

C.

x28x15=0

D.

x2+2x+15=0

Correct answer is B

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

4x24x15=0

Divide through by 4

=x2x154=0

=x2x+(154)=0

=x2(1)x+(154)=0

sum of roots =1

= m + (m + 4) = 1
=2m+4=1

=2m=-3

=m=-32

The equation whose roots are 2m and 2m+8

2m=2×-32=3and 2m+8=2×32+8=5

=x2(3+5)x+(3)(5)=0

=x22x+(15)=0

∴x^2-2x-15=0