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If a and b are roots of the equation x $2$ + a x + b = 0, then a + b =

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-1

answer is D.

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Detailed Solution

Given x

2

+ a x + b = 0
If the roots of

a x 2 + b x 2 + c

with

a ≠ 0

are α and β, then:

⇒ α + β = − b a ⇒ α β = c a

If α and β are roots then:

(x − α) (x − β) = 0

which can be written as

x 2 − (α + β) x + α β = 0

a and b are the roots of the equation

x 2 + a x + b = 0

Compare the given equation with

a x 2 + b x + c = 0

.
Here a = 1, b = a, c = b.

Sum of zeros = − b a ⇒ a + b = − b a ⇒ a + b = − a 1

Sum of zeroes,

a + b = − a

Write value of b in terms of a.

b = − a − a ⇒ b = − 2 a … … … … … … … . (1)

Write the formula for the product of zeroes.

⇒ a × b = c a ⇒ a b = b 1

Product of zeroes,

a b = b

Write value of a in terms of b.

a = b b ⇒ a = 1

Substitute value of a = 1 in equation (i).

⇒ b = − 2 a ⇒ b = − 2 (1) ⇒ b = − 2

Now,

⇒ a + b = 1 − 2 ⇒ a + b = − 1

Hence, the correct option is 4.

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