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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

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)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

y < 0 \forall x \in (- \infty, α)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

y < 0 \forall x \in (β, \infty)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

y = 0 \forall x \in {α, β}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

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.

Suggest Corrections

Similar questions

Q. For any quadratic expression

f (x) = a x^{2} + b x + c; a < 0

, having zeros as

α, β

and if

k

is any real number such that

k < β < α,

then select the correct statement(s).

Q. If both the roots

α, β

of the quadratic equation

a x^{2} + b x + c = 0, a < 0

are less than a real number

k

such that

k > α > β

Considering

f (x) = a x^{2} + b x + c

, select the correct statement(s).

If $α, β$ are the roots of the equation $a x^{2} + b x + c = 0$ such that $β < α < 0,$ then the quadratic equation whose roots are $| α |, | β |$ is given by

Q. If

α, β

are the roots of the quadratic equation

a x^{2} + b x + c = 0, a \neq 0,

then select the correct pair.

Q. If roots of the equation

f (x + 2) = a x^{2} + b x + c = 0

and

α, β

are such that

α < - 2 < β

, then for the equation

f (x) = A x^{2} + B x + C

Join BYJU'S Learning Program

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.