Answer:
6x2 – 7x + 2 = 0 has real roots
The roots are 2/3 and 1/2
Step-by-step explanation:
If a quadratic equation has real roots then the discriminant (b² - 4ac ) is a positive value.
The given quadratic equation be, 6x2 – 7x + 2 = 0
To find discriminant
a = 6 , b = -7 and c = 2
b² - 4ac = (-7)² - (4*6*2) = 49 - 48 = 1
Therefore discriminant is positive,
so he equation 6x2 – 7x + 2 = 0 has real roots
Find the roots by the method of completing the squares
Let 6x2 – 7x + 2 = 0
⇒ 6x2 – 7x = -2
⇒x2 – 7x/6 = -2/6
Here b = -7/6
b/2 = -7/12
Adding both sides by (-7/12)²
x2 – 7x/6 = -2/6
⇒x2 – 7x/6 +(-7/12)² = -2/6 +(-7/12)²
⇒x2 – 7x/6 +(-7/12)² = -2/6 + 49/144
(x - 7/12)² = -48/144 + 49/144
(x - 7/12)² = 1/144
x - 7/12 = √( 1/144 )
x - 7/12 = ± 1/12
x = 1/12 + 7/12 or x = -1/12 + 7/12
x = 8/12 = 2/3 or x = 6/12 = 1/2
x = 2/3 or x = 1/2
