If the polynomial g(x) = x^2 + bx + c has a double root, what can be inferred ab

If the polynomial g(x) = x^2 + bx + c has a double root, what can be inferred about its discriminant?

If the polynomial g(x) = x^2 + bx + c has a double root, what can be inferred about its discriminant?

Step 1: Understand what a polynomial is. A polynomial is a mathematical expression that includes variables and coefficients, like g(x) = x^2 + bx + c.
Step 2: Identify what a double root means. A double root occurs when a polynomial touches the x-axis at one point and does not cross it, meaning it has a repeated solution.
Step 3: Learn about the discriminant. The discriminant is a value calculated from the coefficients of the polynomial, specifically from the formula D = b^2 - 4ac, where a, b, and c are the coefficients of the polynomial.
Step 4: Know the significance of the discriminant. The discriminant helps determine the nature of the roots of the polynomial. If D > 0, there are two distinct roots; if D = 0, there is one double root; and if D < 0, there are no real roots.
Step 5: Conclude that if the polynomial g(x) has a double root, then its discriminant must be equal to zero (D = 0).

Discriminant of a Polynomial – The discriminant of a quadratic polynomial ax^2 + bx + c is given by the formula D = b^2 - 4ac. It determines the nature of the roots of the polynomial.
Double Roots – A polynomial has a double root when it touches the x-axis at a single point, which occurs when the discriminant is zero.