Check whether the equation 5x² - 6x - 2 = 0 has equal roots and if it has, Find them by the method of completing the square. Answer Fast!!
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Discriminant = b2 – 4ac
= 36 – 4 × 5 × (–2)
= 76 > 0
So, the given equation has two distinct real roots.
5x2 – 6x – 2 = 0
Multiplying both sides by 5.
(5x)2 – 2 × (5x) × 3 = 10
(5x)2 – 2 × (5x) × 3 + 32 = 10 + 32
(5x – 3)2 = 19
5x – 3 = ±√19
x = (3 ± √19)/5
Hope This Helps :)
ExoticExplorer:
Ok, see this, a simpler solution:
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.
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.
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