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Find the roots by the factorisation method 2/5 x^2 - x - 3/5 = 0
Answers
Step-by-step explanation:
2/5 x^2 - x - 3/5 = 0
multiply both sides with 5.
so,
5[2/5 x^2 - x - 3/5] = 5[0].
=》 2x^2-5x-3 = 0.
Factoring 2x2-5x-3 = 0.
The first term is, 2x^2 its coefficient is 2 .
The middle term is, -5x its coefficient is -5 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -6
Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -5 .
-6 + 1 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 1
2x2 - 6x + 1x - 3
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x-3)
Add up the last 2 terms, pulling out common factors :
1 • (x-3)
Step-5 : Add up the four terms of step 4 :
(2x+1) • (x-3)
Which is the desired factorization
2x+1 = 0 (or) x-3 = 0.
2x = -1 (or) x=3.
x= -1/2 (or) x = 3.
therefore -1/2 & 3 are the roots of the 2/5 x^2 - x - 3/5 = 0
Answer:2x² / 5 - x/1 - 3/5 = 0
By Taking LCM ,
=2x² - 5x - 3 = 5* 0
=2 x² - 5x - 3 = 0
By Prime factorisation
= { (2x²) * (-3)= -6x² , also -6x ² = - 6x * 1 x , and -6x + 1x = -5x }
=2 x² - 6x + 1 x + 3 = 0
=2x ( x -3 ) +1 ( x + 3 ) = 0
=(2x+1 ) ( x - 3 ) = 0
=2x + 1 = 0 or x -3 = 0
=x = - 1 / 2 or x = 3
x = - 1 / 2 and 3
ROOTS of above quadratic equation are -1/2 and 3.