Math, asked by manasviinjetty2, 20 days ago

) Determine whether the gives values of x is the root of given quadratic equation 6x2 - x - 2 = 0, x = 3/2​

Answers

Answered by achyuthvdev1
0

Step-by-step explanation:

Solution:

The given quadratic equation is 6x2 – x – 2 = 0

Let, x = - ½

∴ 6(- ½ )2 – (- ½ ) – 2 = 0

∴ 6 (1/4) + 1/2 – 2 = 0

∴ 3/2 + ½ - 2 = 0

∴ 4/2 - 2 = 0

∴ 2 – 2 = 0

∴ 0 = 0

Since the value of – ½ satisfies the given quadratic equation

∴ It is the root of the given quadratic equation.

Let, x = 2/3

∴ 6(2/3)2 – (2/3) – 2 = 0

∴ 6(4/9) – 2/3 – 2 = 0

∴ 8/3 – 2/3 – 2 = 0

∴ 6/3 – 2 = 0

∴ 2 – 2 = 0

∴ 0 = 0

Since the value of 2/3 satisfies the given quadratic equation

∴ It is the root of the given quadratic equation.

Let, x = 3/2 ,

∴ 6(3/2)2 – (3/2) – 2 = 0

∴ 6(9/4) – 3/2 – 2 = 0

∴ 27/2 – 3/2 – 2 = 0

∴ 24/2 – 2 = 0

∴ 12 – 2 = 0

∴ 10 ≠ 0

Since the value of 3/2 does not satisfy the given quadratic equation

∴ It is not the root of the given quadratic equation.

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