Find the discriminant for the following quadratic equations. Also, determine the nature of the roots.
(i) 5x²–6x–2=0
(ii) x²-3√3x+12=0
Answers
Answered by
3
Answer:
Step-by-step explanation:
D= b²-4ac is called discriminant.
The nature of roots depend upon the value of the discriminant D. Since D can be zero, positive or negative.
When D>0
If D= b²-4ac >0, then
x= -b+√D/2a & -b-√D/2a
So, the quadratic equation has two distinct real roots.
[ SOLUTION IS IN THE ATTACHMENT]
Verification:
5x²-6x-2=0
5{(3+√19)/5)}² - 6 (3+√19)/5 -2=0
5(9+6√19+19/25) - (18+6√19)/5 -2=0
(9+6√19+19)/5 - (18+6√19)/5 -2=0
(9+6√19+19)/5 - (18+6√19)/5 -2=0
(9+6√19+19)/5 - 18-6√19/5 -2=0
(9 - 18+19+6√19-6√19)/5 -2=0
(-9+19)/5 -2=0
(10/5)-2=0
2-2= 0
0= 0
L.H.S = R.H.S
Similarly we can prove that
5{(3-√19)/5)}² - 6 (3-√19)/5 -2= 0
Answered by
1
Answer:
sorry mate I am bit busy now
Step-by-step explanation:
i promise that I'll surely thank you 15 answers ...later
sorry sorry.....
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