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If the roots of the quadratic polynomial...

If the roots of the quadratic polynomial are equal, are the discriminant `D=B^2-4AC`, then:

A

`Dgt0`

B

`Dlt0`

C

`Dge0`

D

`D=0`

Text Solution

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The correct Answer is:
To determine the condition under which the roots of a quadratic polynomial are equal, we start with the standard form of a quadratic polynomial: \[ P(x) = Ax^2 + Bx + C \] The discriminant \( D \) of this polynomial is given by the formula: \[ D = B^2 - 4AC \] ### Step 1: Understand the condition for equal roots For a quadratic polynomial, the roots are equal (or repeated) if and only if the discriminant \( D \) is equal to zero. ### Step 2: Set the discriminant to zero To find the condition for equal roots, we set the discriminant to zero: \[ B^2 - 4AC = 0 \] ### Step 3: Rearranging the equation Rearranging the equation gives us: \[ B^2 = 4AC \] ### Conclusion Thus, the condition for the roots of the quadratic polynomial \( Ax^2 + Bx + C \) to be equal is: \[ D = B^2 - 4AC = 0 \] ### Summary If the roots of the quadratic polynomial are equal, then the discriminant \( D \) must be zero. ---
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