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Question

# For any quadratic equation y=ax2+bx+c, with roots as α,β such that α<β if a<0 & D>0, then select the correct statements.

A
y>0 x(α,β)
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B
y<0 x(,α)
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C
y<0 x(β,)
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D
y=0 x{α,β}
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Solution

## The correct option is D y=0 ∀ x∈{α,β}Given the quadratic equation: y=ax2+bx+c with roots α,β such that α<β. Also, a<0 & D>0 Thus, we can draw the general graph of the function as: Now as from the graph, we can observe: y>0 ∀ x∈(−∞,α)∪(β,∞)& y<0 ∀ x∈(α,β)& y=0 ∀ x∈{α,β} Thus, all options are correct.

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