Maths

So, the value of x 2 – 3 is zero when x = 3 or x = – 3☞
30 MATHEMATICS
b (Coefficient of x)
✂
i.e., sum of zeroes = + ✁ =
2
a Coefficient of x
✂ ✄ ,
product of zeroes = ✁ =
Let us consider some examples.
c
a
Constant term
Coefficient of x
☎ .
2
Example 2 : Find the zeroes of the quadratic polynomial x 2 + 7x + 10, and verify the
relationship between the zeroes and the coefficients.
Solution : We have
x 2 + 7x + 10 = (x + 2)(x + 5)
So, the value of x 2 + 7x + 10 is zero when x + 2 = 0 or x + 5 = 0, i.e., when x = – 2 or
x = –5. Therefore, the zeroes of x 2 + 7x + 10 are – 2 and – 5. Now,
(7) – (Coefficient of x
✂
)
sum of zeroes = ✆ –2 ✄ (–5) ✄ ✄
–(7)
,
2
1 Coefficient of x
10 Constant term
product of zeroes = ( 2) ( 5) 10
2
1 Coefficient of x
✂ ✝ ✂ ✄ ✄ ✄ ✞
Example 3 : Find the zeroes of the polynomial x 2 – 3 and verify the relationship
between the zeroes and the coefficients.
Solution : Recall the identity a 2 – b 2 = (a – b)(a + b). Using it, we can write:
x
x 2 – 3 ✟ ✠ ✟ ✠
= 3 x 3
✡
☛
Therefore, the zeroes of x 2 – 3 are 3 and ✌ ☞ 3
Now,
sum of zeroes =
3 3 0
✂ ✄ ✄
(Coefficient of x) ,
2
Coefficient of x
✂
3 Constant term
✂
✎✍ ✎ product of zeroes = 3 3 –3
2
✍
1 Coefficient of x
✂ ✄ ✄ ✄ ✞