Question

If the roots of the equation ax² + bx + c = 0 with a ≠ 0 are real and have roots α and -α, then
1. b = 0
2. c = -α2a
3. b = 0 and c = αa
4. Both option 1 and 2 are correct

Answer 1

Correct Answer - Option 4 : Both option 1 and 2 are correct

Concept:

The roots of a quadratic equation ax2 + bx + c = 0

\(\rm x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

• The sum of the roots = \(\rm -b\over a\)
• The product of the roots = \(\rm c\over a\)

Calculation:

Given quadratic equation:

ax2 + bx + c = 0

Roots are 

Now the sum of the roots = \(\rm -b\over a\)

α + -α = \(\rm -b\over a\)

0 = \(\rm -b\over a\)

b = 0

Also product of the roots = \(\rm c\over a\)

α × -α = \(\rm c\over a\)

-α² = \(\rm c\over a\)

c = -α²a