Question

The formula for finding the roots of quadratic equation is _____.

• A. \(\dfrac{b \pm \sqrt{b^2-4ac}}{2a}\)
• B. \(\dfrac{b-\sqrt{b^2-4ac}}{2a}\)
• C. \(\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\)
• D. \(\dfrac{-b \pm \sqrt{b^2+4ac}}{2a}\)

Hint:

Always remember the quadratic formula in this exact order: \[ \frac{-b \pm \sqrt{b^2-4ac}}{2a} \] Students commonly forget:
• the negative sign before \(b\)
• or write \(b^2+4ac\) instead of \(b^2-4ac\) So be extra careful with signs.

Answer 1

The Correct Option is C

Concept: A quadratic equation is an equation of degree 2 and is written in the standard form: \[ ax^2+bx+c=0 \] where:
• \(a,b,c\) are constants
• \(a \neq 0\) The roots (solutions) of the quadratic equation are obtained using the quadratic formula.

Step 1: Write the standard quadratic equation. \[ ax^2+bx+c=0 \] The solutions of this equation are values of \(x\) that satisfy the equation.

Step 2: Recall the quadratic formula. The general formula for roots of a quadratic equation is: \[ x= \frac{-b\pm\sqrt{b^2-4ac}}{2a} \] This formula gives:
• one root using \(+\)
• another root using \(-\)

Step 3: Understand the discriminant. The term: \[ b^2-4ac \] is called the discriminant. It determines the nature of roots.
• If: \[ b^2-4ac>0 \] roots are real and distinct.
• If: \[ b^2-4ac=0 \] roots are equal.
• If: \[ b^2-4ac<0 \] roots are imaginary.

Step 4: Compare with the options. Option (3): \[ \frac{-b \pm \sqrt{b^2-4ac}}{2a} \] matches the standard quadratic formula exactly. Final Answer: \[ \boxed{\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}} \]