Question

whose roots are decreased by 1 than those of 2x^2-3x+1 is​

Answer 1

Answer:

This one is a bit long. So hold on for a couple of minutes while I take you an a ride of this magical land.

Suppose the roots are

α,β,γ,δ

So,according to the relation between the coefficients and roots,we get,

α+β+γ+δ=−8

αβ+βγ+γδ+δα+αγ+βδ=834

αβγ+βγδ+γδα+δαβ=−19

αβγδ=214

So,the roots of the wanted equation will be

α+2,β+2,γ+2,δ+2

(α+2)(β+2)(γ+2)(δ+2)

=αβγδ+2(αβγ+βγδ+γδα+δαβ)+4(αβ+βγ+γδ+δα+αγ+βδ)+8(α+β+γ+δ)+16

=214+2.−19+83−8.8+16

=94

Now,

(α+2)(β+2)(γ+2)+(β+2)(γ+2)(δ+2)+(γ+2)(δ+2)(α+2)+(δ+2)(α+2)(β+2)

=αβγ+βγδ+γδα+δαβ+2.2[αβ+βγ+γδ+δα+αγ+βδ]+4.2[α+β+γ+δ]+32

=−19+83+4.3.−8+32

=0

(α+2)(β+2)+(β+2)(γ+2)+(γ+2)(δ+2)+(δ+2)(α+2)+(α+2)(γ+2)+(β+2)(δ+2)

=αβ+βγ+γδ+δα+αγ+βδ+2.3[α+β+γ+δ]+24

=834−2.3.8+24

=−134

α+2+β+2+γ+2+δ+2

=−8+8

=0

So,the wanted equation is

x4−(0)x3+(−134)x2−(0)x+94=0

SO, 4x4−13x2+9=0

Answer 2

Answer:

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