Question

if alpha beta gamma are the zeros of x³-5x²-2x+24 and alpha×beta=12 then gamma=? a.2 b.-2 c.3 d.-3​

Answer 1

Answer:

Hi mate,

solution: x³-5x²-2x+24

compare with ax³+bx²+cx+d

α+β+y=-b/a

=5

αβy=-d/a

=-24

12y= -24

(as given the product of two. zeros ie αβ=12)

y= -2.

α+β+y=5

α+β-2=5

α+β =7. .................(1)

(α+β)²=7²

(α-β)²+4αβ=49

(α-β)²+4*12=49

(α-β)²+48= 49

(α-β)² =1

α-β = √1

α-β=1. ....................(2)

subtracting (2) From (1)

α+β-(α-β)=7-1

α+β-α+β=6

2β =6

β=3

putting the value of β in the (2) eq

α-3=1

α=4

α=4,β=3,y=-2

product of α and β = 4 * 3 = 12

and difference of α and β = 4 - 3 = 1

I hope it helps you.

Read more on Brainly.in - https://brainly.in/question/10163572#readmoreHi mate,

solution: x³-5x²-2x+24

compare with ax³+bx²+cx+d

α+β+y=-b/a

=5

αβy=-d/a

=-24

12y= -24

(as given the product of two. zeros ie αβ=12)

y= -2.

α+β+y=5

α+β-2=5

α+β =7. .................(1)

(α+β)²=7²

(α-β)²+4αβ=49

(α-β)²+4*12=49

(α-β)²+48= 49

(α-β)² =1

α-β = √1

α-β=1. ....................(2)

subtracting (2) From (1)

α+β-(α-β)=7-1

α+β-α+β=6

2β =6

β=3

putting the value of β in the (2) eq

α-3=1

α=4

α=4,β=3,y=-2

product of α and β = 4 * 3 = 12

and difference of α and β = 4 - 3 = 1

I hope it helps you.

Read more on Brainly.in - https://brainly.in/question/10163572#readmoreHi mate,

solution: x³-5x²-2x+24

compare with ax³+bx²+cx+d

α+β+y=-b/a

=5

αβy=-d/a

=-24

12y= -24

(as given the product of two. zeros ie αβ=12)

y= -2.

α+β+y=5

α+β-2=5

α+β =7. .................(1)

(α+β)²=7²

(α-β)²+4αβ=49

(α-β)²+4*12=49

(α-β)²+48= 49

(α-β)² =1

α-β = √1

α-β=1. ....................(2)

subtracting (2) From (1)

α+β-(α-β)=7-1

α+β-α+β=6

2β =6

β=3

putting the value of β in the (2) eq

α-3=1

α=4

α=4,β=3,y=-2

product of α and β = 4 * 3 = 12

and difference of α and β = 4 - 3 = 1

hope it helps you.

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