All possible values of expression $x^{2} - 4 x + 9$ is

( $- \infty$ ,9]

No worries! We‘ve got your back. Try BYJU‘S free classes today!

( $- \infty$ ,-9]

No worries! We‘ve got your back. Try BYJU‘S free classes today!

(5, $\infty$ )

No worries! We‘ve got your back. Try BYJU‘S free classes today!

[5, $\infty$ )

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

Open in App

Solution

The correct option is D
[5, $\infty$ )

$x^{2} - 4 x + 9 =$ $x^{2} - 2 (2) x + 4 - 4 + 9$

$= (x - 2)^{2} + 5$

We know that ${(x - 2)}^{2} \geq 0$

$(x - 2)^{2} + 5 \geq 5$
(or)

$\infty$ > $(x - 2)^{2} + 5 \geq 5$

$\Rightarrow$ $(x - 2)^{2} + 5 \in [5, \infty)$

Suggest Corrections

Similar questions

All possible values of expression $x^{2} - 4 x + 9$ is

The interval that gives all possible values of the expression $\sqrt{x^{2} - 4 x + 20}$ is

x \in R - {3},

\frac{\sqrt{x^{2} - 6 x + 9}}{3 - x} + 2

x

\frac{x}{x^{2} - 5 x + 9}

Join BYJU'S Learning Program