If x is real and x2-3 x-2-0- x2-3 x-4 - 0- then which one of the following is correct- A- -1 - x - 4B- -1 - x-1 or 2-x - 4C- -1-x - 1D- 2 - x - 4

The correct option is B 1 ≤ x lt; 1 or 2 lt; x ≤ 4Consider first : x^2 3x + 2 gt; 0 ⇒ (x 1)(x 2) gt; 0 ⇒ x lt; 1 or x gt; 2 ...(1) A ...

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

Byju's Answer

Other

Quantitative Aptitude

Solving Inequalities

If x is real ...

Question

If x is real and $x^{2} - 3 x + 2 > 0, x^{2} - 3 x - 4 \leq 0,$ then which one of the following is correct ?

- 1 \leq x \leq 4

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

2 \leq x \leq 4

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

- 1 < x \leq 1

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

- 1 \leq x < 1 o r 2 < x \leq 4

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

Open in App

Solution

The correct option is D $- 1 \leq x < 1 o r 2 < x \leq 4$
Consider first : $x^{2} - 3 x + 2 > 0$
$\Rightarrow (x - 1) (x - 2) > 0$
$\Rightarrow x < 1 o r x > 2$ ...(1)
And $x^{2} - 3 x - 4 \leq 0$
$\Rightarrow (x - 4) (x + 1) \leq 0$
$\Rightarrow - 1 \leq x \leq 4$ ...(2)
Combining (1) and (2)
$- 1 \leq x < 1 o r 2 < x \leq 4$
Drawing on number line :

Suggest Corrections

Similar questions

Say true or false.

x^{2} - 3 x + 2 = 0

, then

x = 2

x = 1

Q. The number of real roots of the equation

\frac{x^{2} - 3 x}{x^{2} - 1} + 2 + \frac{1}{x - 1} = 0

Q. All real values of

x

which satisfy

x^{2} - 3 x + 2 > 0

and

x^{2} - 3 x - 4 \leq 0

lie in the interval

Question 9
Which of the following equation has two distinct real roots?
(a) $2 x^{2} - 3 \sqrt{2} x + \frac{9}{4} = 0$
(b) $x^{2} + x - 5 = 0$
(c) $x^{2} + 3 x + 2 \sqrt{2} = 0$
(d) $5 x^{2} - 3 x + 1 = 0$

Q. Length and width of rectangle are

(x + 4)

(x - 1)

, then the area of the rectangle is.

Join BYJU'S Learning Program

If x is real and x2−3x+2>0,x2−3x−4≤0, then which one of the following is correct ?

The correct option is D −1≤x<1 or 2<x≤4Consider first : x2−3x+2>0 ⇒(x−1)(x−2)>0 ⇒x<1 or x>2 ...(1) And x2−3x−4≤0 ⇒(x−4)(x+1)≤0 ⇒−1≤x≤4 ...(2) Combining (1) and (2) −1≤x<1 or 2<x≤4 Drawing on number line :

If x is real and $x^{2} - 3 x + 2 > 0, x^{2} - 3 x - 4 \leq 0,$ then which one of the following is correct ?