find the roots of the equation 2x^2-5x+3=0 and verify whether 1 and 3/2 are the roots of the equation.
Answers
x=1,x=3/2
Step-by-step explanation:
2x²-5x+3=0
0=2x²-3x-2x+3
0=x(2x-3)-1(2x-3)
0=(x-1)(2x-3)
if x-1=0
x=1
if 2x-3=0
then 2x=3
x=3/2
Verification:
1)L.H.S.=2(1)²-5(1)+3
=2-5+3
=5-5
=0=R.H.S
2)L.H.S.=2(3/2)²-5(3/2)+3
={2(9/4)}-{15/2}+3
=9/2-15/2+3
=-6/2+3
=-3+3
=0=R.H.S.
Hence Verified
EXPLANATION.
roots of the equation = 2x² - 5x + 3 = 0
verify wheather 1 and 3/2 are the roots of the
equation.
Factories into middle term split.
= 2x² - 5x + 3 = 0
= 2x² - 3x - 2x + 3 = 0
= x ( 2x - 3 ) - 1 ( 2x + 3 ) = 0
= ( x - 1 ) ( 2x - 3 ) = 0
= x = 1 and x = 3/2.
sum = 1 + 3/2
= 2 + 3 /2 = 5/2
products = 1 X 3/2 = 3/2.
sum of zeroes of quadratic equation.
= a + b = -b/a
= a + b = 5/2
products of zeroes of quadratic equation.
= ab = c/a
= ab = 3/2.
More information.
= D > 0 Or [ b² - 4ac > 0 ]
roots are real and unequal.
= D = 0 Or [ b² - 4ac = 0 ]
roots are real and equal.
= D < 0 or [ b² - 4ac < 0 ]
roots are imaginary.