QUADRATIC EQUATIONS
viii) 10x2 + 3x - 4 = 0
10x2 + 3x - 4 = 0
Sol:
Standard form
To factorise by splitting middle term
Find product of 3rd no. with 1st no.
4 × 10 = 40
Find two factors of 40 in such a way
that by subtracting factors we get middle no.
= 1 × 40
40 – 1 ≠ 3
1
40
Since, last sign is –
Give middle sign only to bigger factor & opposite sign to smaller factor
3rd no.
1st no.
middle no.
∴ 10x2 + 8x – 5x – 4 = 0
∴ 2x
(5x + 4)
– 1
(5x + 4)
= 0
∴ (5x + 4) (2x – 1) = 0
∴ 5x + 4 = 0 or 2x – 1 = 0
∴ 5x = – 4 or 2x = 1
= 2 × 20
= 4 × 10
= 5 × 8
40
20 – 2 ≠ 3
2
20
4
10
8 – 5 = 3
8
5
–
+
Now signs to be given to both factors
Product of two brackets is zero
Either (5x + 4) = 0 or (2x - 1) = 0
Factorise by splitting middle term
Q) Solve the following quadratic equations by factorization method
10 – 4 ≠ 3
‘–’ sign means subtracting
homework
Find product of 3rd no. with 1st no.
Find two factors of 9 in such a way
that by adding
factors we get middle no.
Since, last sign is +
Give middle sign to both factors.
Q) Solve the following quadratic equations by factorization method
Sol :
Multiplying throughout by 9, we get,
∴ x2 –
∴ x2 – 3x – 3x + 9 = 0
∴ x (x – 3)
∴ (x – 3) = 0 or (x – 3) = 0
∴ (x – 3) (x – 3) = 0
6x +
9 = 0
To Remove ‘9 & 3’ from denominator multiply by LCM of 9 & 3
LCM of 9 & 3 is 9
3
9
3
3
–
–
From first two ‘x’ is common
– 3 (x – 3) = 0
From last two ‘3’ is common along with 3rd term sign
‘+’ sign means adding