An algebra problem by vishwathiga jayasankar
Algebra
Level
3
Which of the following is a possible zero of the quadratic polynomial whose sum and product of zeros are -1 and -20, respectively?
5
3
2
4
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1 solution
If the roots of the quadratic equation are y and z, then:
y + z = − 1 ⟺ z = − ( y + 1 )
y z = − 2 0
− y ( y + 1 ) = − 2 0
y ( y + 1 ) = 2 0
y 2 + y − 2 0 = 0
( y + 5 ) ( y − 4 ) = 0
From the equation above, we get our 2 roots: -5 and 4
Since -5 is not amongst the options, therefore our choice should be:
4