Question

3. Find the roots of the quadratic equation 6x + 7x​

Answer 1

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Answer 2

Mark me BRAINLIEST

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