Question
Solve equation using factorisation method:$2x^2 - 9x + 10 = 0$, When
(i) $x\in N$
(ii) $x\in Q$
(i) $x\in N$
(ii) $x\in Q$
✓
Answer
$2x^2 - 9 + 10 = 0$
$\Rightarrow 2 x^2-5 x-4 x+10=0$
$\Rightarrow x(2 x-5)-2(2 x-5)=0$
$\Rightarrow(2 x-5)(x-2)=0$
$\Rightarrow 2 x-5=0 \text { or } x-2=0$
$\Rightarrow x=\frac{5}{2} \text { or } x=2$
(i) when $x \in N$ we have $x =2$
(ii) When $x \in Q$ we have $x =2, \frac{5}{2}$
$\Rightarrow 2 x^2-5 x-4 x+10=0$
$\Rightarrow x(2 x-5)-2(2 x-5)=0$
$\Rightarrow(2 x-5)(x-2)=0$
$\Rightarrow 2 x-5=0 \text { or } x-2=0$
$\Rightarrow x=\frac{5}{2} \text { or } x=2$
(i) when $x \in N$ we have $x =2$
(ii) When $x \in Q$ we have $x =2, \frac{5}{2}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Cards marked with numbers 1, 2, 3 ……… 20 are well shuffled and a card is drawn at random. What is the probability that the number on the card is: a perfect square
A card is drawn from a pack of 52 cards. Find the probability that the card drawn is : not a club
Evaluate:
$\frac{\cos 70^{\circ}}{\sin 20^{\circ}}+\frac{\cos 59^{\circ}}{\sin 31^{\circ}}-8 \sin ^2 30^{\circ}$
→$\frac{\cos 70^{\circ}}{\sin 20^{\circ}}+\frac{\cos 59^{\circ}}{\sin 31^{\circ}}-8 \sin ^2 30^{\circ}$
Part of geometrical figure is given in each of the diagrams below. Complete the figures, so that the line ‘m’, in each case, is the line of symmetry, of the completed figure. Recognizable free hand sketches, would be awarded full marks.
Two equal circles intersect in P and Q. A straight line through P meets the circles in A and B. Prove that QA = QB
In the given figure, $AD = AE$ and $AD^2 = BD x EC$.
Prove that: triangles $ABD$ and $CAE$ are similar.
→Prove that: triangles $ABD$ and $CAE$ are similar.
Prove the following identity:
$
\frac{1+\sin A}{1-\sin A}=\frac{\operatorname{cosec} A+1}{\operatorname{cosec} A-1}
$
→$
\frac{1+\sin A}{1-\sin A}=\frac{\operatorname{cosec} A+1}{\operatorname{cosec} A-1}
$
Prove.$\frac{\cot ^2 A}{(\operatorname{cosec} A+1)^2}=\frac{1-\sin A}{1+\sin A}$
→Find if x = – 1 is a root of the equation $2x^2 – 3x + 1 = 0.$
→Find the distance between the following pairs of point in the coordinate plane :
$(4 , 1)$ and $(-4 , 5)$
→$(4 , 1)$ and $(-4 , 5)$