QUADRATIC EQUATIONS
Q) Solve the following quadratic equations by factorization method
Since, last sign is –
Give middle sign only to bigger factor and opposite sign to smaller factor
iv) x2 – x – 132 = 0
x2 – x – 132 = 0
Sol:
Standard form
Find product of 3rd no. with 1st no.
1
132 × 1 = 132
132
Find two factors of 132 in such a way
that by subtracting factors we get middle no.
12
11
1
middle no.
Now signs to be given to both factors
–
+
∴ x2 – 12x + 11x – 132 = 0
∴ x(x – 12)
∴ (x – 12) (x + 11) = 0
∴ x – 12 = 0 or x + 11 = 0
From first two ‘x’ is common
From last two ‘11’ is common along with 3rd term sign
+ 11(x – 12) = 0
are 12 and
- 11
Factorise by splitting middle term
Q) Solve the following quadratic equations by factorization method
Since, last sign is –
Give middle sign only to bigger factor.
× = 168
8x2 - 22x - 21 = 0
v) 8x2 – 22x – 21 = 0
Sol:
∴ 8x2 – 28x + 6x – 21 = 0
∴ (2x – 7) (4x + 3) = 0
∴ 2x – 7 = 0 or 4x + 3 = 0
8
21
3 × 7
∴ 4x
(2x – 7)
+ 3
(2x – 7)
= 0
8 can be factorise as
2 × 2 × 2
21 can be factorise as
Take biggest no. as one group
– ≠ 22
24
7
Take biggest no. & one of the smallest as one group
Remaining no. as other group
– ≠ 22
14
12
Take biggest no. & 2 of the smallest as one group
Remaining no. as other group
= 22
28
6
To add or subtract as per last sign
–
+
From first two ‘4x’ is common
From last two ‘3’ is common along with 3rd term sign
Make 2 groups of all factors
Remaining no. as other group