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CGP EDU Academic Team
Published on: August 13, 2026
Graph of x 2 + 6x + k = 0 cuts x-axis at two real and distinct points x 1 and x 2 , while graph of ax 2 + bx + c neither touches nor cuts x-axis, then answer the following
(i) Set of all possible real values of k is
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Ans.
(i)
Sol. Use D > 0
36 – 4k > 0
(ii)
Sol. Let f(x) = ax 2 + bx + c
∴ f(–1) = a + c – b < 0 (given)
So f(1) < 0
∴ a + b + c < 0
(iii)
Sol. x 1 + x 2 = – 6
as x 1 > 0
so x 2 < 0
∴ product of root is negative
∴ f(0) < 0
⇒ k < 0
Now Let f(x) = ax 2 + bx + c
f 
> 0 given
∴ a > 0
So a. k < 0
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