Find a quadratic polynomial whose sum and product respectively of

lugreget9 2021-12-17 Answered
Find a quadratic polynomial whose sum and product respectively of the zeroes are as given also find the zeoes of these polynomial by factorization.
(-8/3) , (4/3)
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Expert Answer

Hector Roberts
Answered 2021-12-18 Author has 31 answers
Step 1
Let the roots of a quadratic equation
ax2+bx+c=0 be α and β
So, α+β=ba=83...(1)
αβ=ca=43...(2)
ax2+bx+c=0
a(x2+bax+ca)=0
Step 2
x2(ba)x+ca=0
x2(α+β)x+αβ=0
Substitute 1 and 2 in above
x2(83)x+43=0
3x2+8x+4=0
The quadratic equation is 3x2+8x+4=0
Step 3
3x2+8x+4=0
3x2+2x+6x+4=0
x(3x+2)+2(3x+2)=0
(3x+2)(x+2)=0
x=23,x=2
The roots are 23,2
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