If the roots of the equation x^2 - 7x + 10 = 0 are a and b, what is the value of

₹0.0

Question: If the roots of the equation x^2 - 7x + 10 = 0 are a and b, what is the value of ab? (2021)

Options:

Correct Answer: 10

Exam Year: 2021

Solution:

By Vieta\'s formulas, ab = 10, which is the constant term of the polynomial.

If the roots of the equation x^2 - 7x + 10 = 0 are a and b, what is the value of ab? (2021)

If the roots of the equation x^2 - 7x + 10 = 0 are a and b, what is the value of ab? (2021)

Step 1: Identify the equation given, which is x^2 - 7x + 10 = 0.
Step 2: Recognize that this is a quadratic equation in the form of ax^2 + bx + c = 0.
Step 3: Identify the coefficients: a = 1, b = -7, and c = 10.
Step 4: Understand Vieta's formulas, which tell us that for a quadratic equation, the product of the roots (ab) is equal to the constant term (c) divided by the coefficient of x^2 (a).
Step 5: Since a = 1 and c = 10, we find that ab = c/a = 10/1.
Step 6: Calculate the value of ab, which is 10.

Vieta's Formulas – Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.