Question

If the quadratic equation ax² + 2bx – c = 0 (a ≠ 0) has real and equal roots, then which of the following is true?

पर्याय

• b² = – ac

• b² = 4ac

• b² = ac

• b² = – 4ac

Answer 1

b² = – ac

Explanation:

1. Identify the coefficients

For a general quadratic equation in the form Ax² + Bx + C = 0, the coefficients are the values multiplying each term. Comparing the given equation ax² + 2bx – c = 0 to the standard form, we have:

A = a

B = 2b

C = –c 

2. Apply the condition for equal roots

A quadratic equation has real and equal roots if and only if its discriminant (D) is equal to zero.

The formula for the discriminant is:

D = B² – 4AC

Setting D = 0 for equal roots:

B² – 4AC = 0

3. Substitute and simplify

Substitute the specific coefficients from the given equation into the discriminant formula:

(2b)² – 4(a)(–c) = 0

Perform the algebraic operations

1. Square the first term: 4b²
2. Multiply the constants and variables in the second part: –4 × a × (–c) = + 4ac
3. Combine: 4b² + 4ac = 0

Divide the entire equation by 4:

b² + ac = 0

Rearrange to solve for b²:

b² = –ac