Question

20. If 2 and a are zeroes of x² - 3x +2, then the value of a is
(a) 2
(b) 3
(c) 1
(d) 5
Mathematics

Answer 1

Answer:

Option C

Step-by-step explanation:

Given :-

'2' and 'a' are zeroes of x² - 3x +2

To find :-

Find the value of 'a' ?

Solution :-

Given quardratic polynomial is x²-3x+2

Let P(x) = x²-3x+2

Given zeroes are '2' and 'a'

We know that

If '2' and 'a' are zeroes of P(x) then they satisfies the given polynomial.

=> P(a) = 0

=> a²-3a+2 = 0

=> a²-a-2a+2 = 0

=> a(a-1)-2(a-2) = 0

=> (a-1)(a-2) = 0

=> a-1 = 0 or a-2 = 0

=> a = 1 or a = 2

Therefore, a = 1 or 2

2 is given as one of the zeroes of P(x)

So , The value of a must be 1

a = 1

Alternative Method :-

Given quardratic polynomial is x²-3x+2

Let P(x) = x²-3x+2

On comparing with the standard quadratic polynomial ax²+bx+c then

a = 1

b = -3

c = 2

Given zeroes are '2' and 'a'

We know that

Sum of the zeroes = -b/a

=> 2+a = -(-3)/1

=> 2+a = 3/1

=> 2+a = 3

=> a = 3-2

=> a = 1

or

Product of the zeroes = c/a

=> (2)(a) = 2/1

=> 2a = 2

=> a = 2/2

=> a = 1

Answer:-

The value of a for the given problem is 1

Used formulae:-

→ The standard quadratic polynomial ax²+bx+c

→ Sum of the zeroes = -b/a

→ Product of the zeroes = c/a