what is positive integral root,

Q:- the positive integral root of equation 2x square-7x+6=0 is

To find the positive integral root of the quadratic equation 2x² - 7x + 6 = 0, we can use the quadratic formula or factorization. Let's start by explaining what we mean by a "positive integral root." This term refers to a solution of the equation that is both positive and a whole number (an integer greater than zero).

Finding Roots of the Quadratic Equation

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants. In your case, a = 2, b = -7, and c = 6. We can apply the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Calculating the Discriminant

First, we need to calculate the discriminant (D), which is the part under the square root in the formula:

D = b² - 4ac

Plugging in our values:

• b² = (-7)² = 49
• 4ac = 4 * 2 * 6 = 48
• So, D = 49 - 48 = 1

Finding the Roots

Now that we have the discriminant, we can find the roots:

x = (7 ± √1) / (2 * 2)

This simplifies to:

• x = (7 + 1) / 4 = 8 / 4 = 2
• x = (7 - 1) / 4 = 6 / 4 = 1.5

Identifying the Positive Integral Root

From our calculations, we see that the roots of the equation are 2 and 1.5. Among these, the positive integral root is clearly 2, as it is the only solution that is a whole number greater than zero.

Verification

To ensure our solution is correct, we can substitute x = 2 back into the original equation:

2(2)² - 7(2) + 6 = 2(4) - 14 + 6 = 8 - 14 + 6 = 0

Since the left side equals zero, we have confirmed that x = 2 is indeed a root of the equation.

In summary, the positive integral root of the equation 2x² - 7x + 6 = 0 is 2.