For any quadratic equation y-ax2-bx-c- with roots as - - such that -0- then select the correct statements-

Given the quadratic equation: y=ax^2+bx+c with roots α, β such that α lt;β. Also, a lt;0 & D gt;0 Thus, we can draw the general graph of the function ...

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Standard XII

Mathematics

Plotting Graph of Quadratic Equation

For any quadr...

Question

For any quadratic equation $y = a x^{2} + b x + c,$ with roots as $α, β$ such that $α < β$ if $a < 0 & D > 0,$ then select the correct statements.

y > 0 \forall x \in (α, β)

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y < 0 \forall x \in (- \infty, α)

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y < 0 \forall x \in (β, \infty)

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y = 0 \forall x \in {α, β}

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Solution

The correct option is D $y = 0 \forall x \in {α, β}$
Given the quadratic equation: $y = a x^{2} + b x + c$ 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:
$y > 0 \forall x \in (- \infty, α) \cup (β, \infty) & y < 0 \forall x \in (α, β) & y = 0 \forall x \in {α, β}$
Thus, all options are correct.

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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.

For any quadratic equation $y = a x^{2} + b x + c,$ with roots as $α, β$ such that $α < β$ if $a < 0 & D > 0,$ then select the correct statements.