If the roots are said to be equal roots, then D = 0.

We are expecting to find the value of "b". So, by using the discriminant formula, we can find the value of "b".

D = b² - 4ac.

Put 0 in the place of D.
(Because, as per the question, it has equal roots. So D is equal to the 0).

0 = b² - 4ac.

Shift 4ac to the left side as we want to find the value of b.

4ac = b².

Apply the square from the b² to the 4ac.
It becomes 2√ac = b.

So, the value of b is 2√ac.

Explanation:

When a quadratic equation has equal roots, it means that the discriminant of the equation is zero. The discriminant of a quadratic equation of the form ax² + bx + c = 0 is given by the expression b² - 4ac. If the discriminant is zero, then the roots of the quadratic equation are equal.

Calculation:

Given that ax² + bx + c = 0 has equal roots. Therefore, the discriminant of the equation is zero.

b² - 4ac = 0

Substituting the value of discriminant in the above equation, we get:

b² - 4ac = 0

b² - 4(a)(c) = 0

b² = 4ac

Conclusion:

From the above expression, we can see that the value of b is dependent on the values of a and c. If either a or c is zero, then we cannot determine the value of b. However, if both a and c are non-zero, then we can solve for b by taking the square root of both sides of the equation:

b = ±√(4ac)

Therefore, the value of b is ±2√(ac) when ax² + bx + c = 0 has equal roots.