Question

dear mates can uh help me....plzzzi in the both questions ​

Answer 1

$\huge\fbox\bold\red{ANSWER}$

$\huge\fbox\bold\red{Question=>(1)}$

(I)2x²-3x+5=0

Here ,a=2,b=-3,c=5

D=b²-4ac

=>(-3)²-4×2×5

=>9-40

=>-31

here d<0

This implies that it has no real roots.

(ii)3x²-4√3+4=0

Here ,a=3,b=-4√3,c=4

D=b²-4ac

=>(-4√3)²-4×3×4

=>16×3-16×3

=>0

here D=0

This implies that it has real and equal roots.

(iii)2x²-6x+3=0

Here ,a=2,b=-6,c=3

D=b²-4ac

=>(-6)²-4×2×3

=>36-24

=>12

here D>0

This implies that it has real and distinct roots.

$\huge\fbox\bold\red{Question=>(2)}$

(I)2x²+Kx+3=0

Here,a=2,b=k,c=3

as roots are equal then

D=0

=>b²-4ac=0

=>k²-4×2×3=0

=>k²-24=0

=>k²=24

k=√24=2√6...ans...

(ii)Kx(x-2)+6=0

=>kx²-2kx+6=0

here,a=k,b=2k,c=6

D=0

=>b²-4ac=0

=>(2k)²-4×k×6

=>4k²-24k=0

=>4k(k-6)=0

$\huge\bold\red{NOW}$

here taking 4k=0

k=0(here k can't be so it's neglected)

and taking k-6=0

k=6

HOPE THIS HELPS U

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THANK U