Graph of f(x) = ax 2 + bx + c is shown adjacently for which…

Maths Quadratic Equations Mix Comprehension

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Graph of f(x) = ax 2 + bx + c is shown adjacently for which λ (AB) = 2, λ (AC) = 3 and b 2 – 4ac = – 4

(i) The value of a + b + c is equal to

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Ans.

(i)

Sol. AB = = 2

⇒ = 2

⇒ a =

AC = 3 ⇒ = –3

⇒ b = 6a = 3

b 2 – 4ac = – 4

⇒ c = 13/2

∴ a + b + c = 10

(ii)

Sol. α = b + = 3 +

so other root is 3 –

∴ equation will be x 2 – 6x + 2 = 0

(iii)

Sol. g (x) = x 2 + 5x – 6

g (– 4) = –10, g (0) = – 6

[g (x)] min. = at x = –5/2

∴ Range of g (x) is

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