Question
Factorise:
$7\text{x}^2+2\sqrt{14}\text{x}+2$
$7\text{x}^2+2\sqrt{14}\text{x}+2$
✓
Answer
$7\text{x}^2+2\sqrt{14}\text{x}+2$
$=7\text{x}^2+\sqrt{2}\big(\sqrt{7}\text{x}\big)+\sqrt{2}\big(\sqrt{7}\text{x}\big)+2$
$=\sqrt{7}\text{x}\big(\sqrt{7}\text{x}+\sqrt{2}\big)+\sqrt{2}\big(\sqrt{7}\text{x}+\sqrt{2}\big)$
$=\big(\sqrt{7}\text{x}+\sqrt{2}\big)\big(\sqrt{7}\text{x}+\sqrt{2}\big)=\big(\sqrt{7}\text{x}+\sqrt{2}\big)^2$
$=7\text{x}^2+\sqrt{2}\big(\sqrt{7}\text{x}\big)+\sqrt{2}\big(\sqrt{7}\text{x}\big)+2$
$=\sqrt{7}\text{x}\big(\sqrt{7}\text{x}+\sqrt{2}\big)+\sqrt{2}\big(\sqrt{7}\text{x}+\sqrt{2}\big)$
$=\big(\sqrt{7}\text{x}+\sqrt{2}\big)\big(\sqrt{7}\text{x}+\sqrt{2}\big)=\big(\sqrt{7}\text{x}+\sqrt{2}\big)^2$
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
ABCD is a rhombus show that diagonal AC bisects $\angle $A as well as $\angle $C and diagonal BD bisects $\angle $B as well as $\angle $D
→Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and two parallels:
Verify whether the indicated numbers are zeros of the polynomials corresponding to them in the following case:
$\text{f(x)}=3\text{x}+1,\text{x}=-\frac{1}{3}$
→$\text{f(x)}=3\text{x}+1,\text{x}=-\frac{1}{3}$
Factorise:
x2 - 4x + 3
x2 - 4x + 3
Factorise:
x2 - 24x - 180
x2 - 24x - 180
In $\Delta\text{ABC,}$ BC = 8cm and CA = 7cm. If D and E are respectively the mid-points of AB and BC, determine the length of DE.
→Read the passage given below and answer the questions:
Dev was doing an experiment to find the radius r of a sphere. For this he took a cylindrical container with radius R = 7cm and height 10cm. He filled the container almost half by water as shown in the left figure. Now he dropped the yellow sphere in the container. Now he observed as shown in the right figure the water level in the container raised from A to B equal to 3.40cm.
1. What is the volume of the sphere?
2. How many litres water can be filled in the full container? ( Take 1 litre = 1000cm3)
Dev was doing an experiment to find the radius r of a sphere. For this he took a cylindrical container with radius R = 7cm and height 10cm. He filled the container almost half by water as shown in the left figure. Now he dropped the yellow sphere in the container. Now he observed as shown in the right figure the water level in the container raised from A to B equal to 3.40cm.
1. What is the volume of the sphere?
2. How many litres water can be filled in the full container? ( Take 1 litre = 1000cm3)
Express the following equation in the form ax + by + c = 0 and indicate the values of a, b, c in case.
→$\sqrt{2}\text{x}+\sqrt{3}\text{y}=5$
BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that a triangle ABC is isosceles.
Can a triangle have:
All angles equal to 60°?
Justify your answer in case.
All angles equal to 60°?
Justify your answer in case.